diff --git a/doc/source/whatsnew/v1.0.5.rst b/doc/source/whatsnew/v1.0.5.rst
index 1edc7e1cad72f..5dbc911407784 100644
--- a/doc/source/whatsnew/v1.0.5.rst
+++ b/doc/source/whatsnew/v1.0.5.rst
@@ -22,7 +22,8 @@ Fixed regressions
 
 Bug fixes
 ~~~~~~~~~
--
+
+- Fixed building from source with Python 3.8 fetching the wrong version of NumPy (:issue:`34666`)
 -
 
 Contributors
diff --git a/pyproject.toml b/pyproject.toml
index efeb24edbdeb1..aaebcff8e4c1e 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -6,9 +6,11 @@ requires = [
     "wheel",
     "Cython>=0.29.16",  # Note: sync with setup.py
     "numpy==1.15.4; python_version=='3.6' and platform_system!='AIX'",
-    "numpy==1.15.4; python_version>='3.7' and platform_system!='AIX'",
+    "numpy==1.15.4; python_version=='3.7' and platform_system!='AIX'",
+    "numpy==1.17.3; python_version>='3.8' and platform_system!='AIX'",
     "numpy==1.16.0; python_version=='3.6' and platform_system=='AIX'",
-    "numpy==1.16.0; python_version>='3.7' and platform_system=='AIX'",
+    "numpy==1.16.0; python_version=='3.7' and platform_system=='AIX'",
+    "numpy==1.17.3; python_version>='3.8' and platform_system=='AIX'",
 ]
 
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