diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index 8d5bde09ea9b5b..a7db1c116f47dd 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -640,9 +640,34 @@ def __sleep0():
     yield
 
 
+def _check_delay(delay):
+    """Check if the value of 'delay' is valid."""
+
+    import sys
+    import math
+
+    SEC_TO_NS = 1000 * 1000 * 1000
+
+    if not isinstance(delay, (int, float)):
+        raise TypeError(f"{type(delay)} object cannot be interpreted as an integer")
+
+    # According to Modules/timemodule.c
+    if (delay > sys.maxsize / SEC_TO_NS):
+        raise OverflowError("timestamp too large to convert to C _PyTime_t")
+
+    if (delay < 0):
+        raise ValueError("sleep length must be non-negative")
+
+    if (math.isnan(delay)):
+        raise ValueError("Invalid value NaN (not a number)")
+
+
 async def sleep(delay, result=None):
     """Coroutine that completes after a given time (in seconds)."""
-    if delay <= 0:
+
+    _check_delay(delay)
+
+    if delay == 0:
         await __sleep0()
         return result
 
diff --git a/Misc/NEWS.d/next/Core and Builtins/2023-06-08-16-29-43.gh-issue-105513.M7ueoq.rst b/Misc/NEWS.d/next/Core and Builtins/2023-06-08-16-29-43.gh-issue-105513.M7ueoq.rst
new file mode 100644
index 00000000000000..91311d9757258f
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2023-06-08-16-29-43.gh-issue-105513.M7ueoq.rst	
@@ -0,0 +1 @@
+fix asyncio.sleep(float('nan')) does not raise ValueError bug