diff --git a/Cargo.lock b/Cargo.lock
index 88b2ffbf6..a987cef6d 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -1266,6 +1266,7 @@ dependencies = [
  "multipart",
  "native-tls",
  "once_cell",
+ "pep440",
  "platform-info",
  "pretty_env_logger",
  "pyproject-toml",
@@ -1629,6 +1630,16 @@ version = "0.2.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "c54014ba3c1880122928735226f78b6f5bf5bd1fed15e41e92cf7aa20278ce28"
 
+[[package]]
+name = "pep440"
+version = "0.2.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "8841b00ca6fabc903e8ecd496d9611db402e23f15e3d19b0b587e2ca653abd89"
+dependencies = [
+ "lazy_static",
+ "regex",
+]
+
 [[package]]
 name = "percent-encoding"
 version = "2.1.0"
diff --git a/Cargo.toml b/Cargo.toml
index bd8bfd105..ce402abac 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -60,6 +60,10 @@ cc = "1.0.72"
 clap = { version = "3.2.16", features = ["derive", "env", "wrap_help"] }
 clap_complete = "3.1.3"
 clap_complete_fig = "3.1.0"
+tracing = "0.1.36"
+dunce = "1.0.2"
+pep440 = "0.2.0"
+
 # upload
 bytesize = { version = "1.0.1", optional = true }
 configparser = { version = "3.0.0", optional = true }
@@ -67,8 +71,6 @@ multipart = { version = "0.18.0", features = ["client"], default-features = fals
 rpassword = { version = "7.0.0", optional = true }
 ureq = { version = "2.3.1", features = ["gzip", "socks-proxy"], default-features = false, optional = true }
 native-tls-crate = { package = "native-tls", version = "0.2.8", optional = true }
-tracing = "0.1.36"
-dunce = "1.0.2"
 
 [dev-dependencies]
 indoc = "1.0.3"
diff --git a/Changelog.md b/Changelog.md
index 682137822..f53683322 100644
--- a/Changelog.md
+++ b/Changelog.md
@@ -11,6 +11,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 * Add Linux mipsel architecture support in [#1024](https://github.com/PyO3/maturin/pull/1024)
 * Add Linux 32-bit powerpc architecture support in [#1026](https://github.com/PyO3/maturin/pull/1026)
 * Add Linux sparc64 architecture support in [#1027](https://github.com/PyO3/maturin/pull/1027)
+* Add PEP 440 local version identifier support in [#1037](https://github.com/PyO3/maturin/pull/1037)
 
 ## [0.13.1] - 2022-07-26
 
diff --git a/src/metadata.rs b/src/metadata.rs
index ae727fc4f..f00dd519c 100644
--- a/src/metadata.rs
+++ b/src/metadata.rs
@@ -408,7 +408,7 @@ impl Metadata21 {
         let mut fields = vec![
             ("Metadata-Version", self.metadata_version.clone()),
             ("Name", self.name.clone()),
-            ("Version", self.get_version_escaped()),
+            ("Version", self.get_pep440_version()),
         ];
 
         let mut add_vec = |name, values: &[String]| {
@@ -505,8 +505,21 @@ impl Metadata21 {
     /// Returns the version encoded according to PEP 427, Section "Escaping
     /// and Unicode"
     pub fn get_version_escaped(&self) -> String {
-        let re = Regex::new(r"[^\w\d.]+").unwrap();
-        re.replace_all(&self.version, "_").to_string()
+        self.get_pep440_version().replace('-', "_")
+    }
+
+    /// Returns the version encoded according to PEP 440
+    ///
+    /// See https://github.com/pypa/setuptools/blob/d90cf84e4890036adae403d25c8bb4ee97841bbf/pkg_resources/__init__.py#L1336-L1345
+    pub fn get_pep440_version(&self) -> String {
+        match pep440::Version::parse(&self.version) {
+            Some(ver) => ver.normalize(),
+            None => {
+                let ver = self.version.replace(' ', ".");
+                let re = Regex::new(r"[^A-Za-z0-9.]+").unwrap();
+                re.replace_all(&ver, "-").to_string()
+            }
+        }
     }
 
     /// Returns the name of the .dist-info directory as defined in the wheel specification
diff --git a/test-crates/pyo3-pure/pyproject.toml b/test-crates/pyo3-pure/pyproject.toml
index 23275d848..4575ddf92 100644
--- a/test-crates/pyo3-pure/pyproject.toml
+++ b/test-crates/pyo3-pure/pyproject.toml
@@ -7,6 +7,7 @@ bindings = "pyo3"
 
 [project]
 name = "pyo3-pure"
+version = "0.1.0+abc123de"
 classifiers = [
     "Programming Language :: Rust"
 ]