diff --git a/babel/dates.py b/babel/dates.py
index 7b626aa11..c197df573 100644
--- a/babel/dates.py
+++ b/babel/dates.py
@@ -1375,14 +1375,18 @@ def parse_time(
     # TODO: support time zones
 
     # Check if the format specifies a period to be used;
-    # if it does, look for 'pm' to figure out an offset.
-    hour_offset = 0
-    if 'a' in format_str and 'pm' in string.lower():
-        hour_offset = 12
+    # if it does, convert the hour from the 12-hour clock, on which
+    # 12 AM and 12 PM are 00:00 and 12:00 respectively.
+    hour = int(numbers[indexes['H']])
+    if 'a' in format_str:
+        if 'pm' in string.lower():
+            if hour != 12:
+                hour += 12
+        elif 'am' in string.lower() and hour == 12:
+            hour = 0
 
     # Parse up to three numbers from the string.
     minute = second = 0
-    hour = int(numbers[indexes['H']]) + hour_offset
     if len(numbers) > 1:
         minute = int(numbers[indexes['M']])
         if len(numbers) > 2:
diff --git a/tests/test_dates.py b/tests/test_dates.py
index 4f8c73907..06a3126c9 100644
--- a/tests/test_dates.py
+++ b/tests/test_dates.py
@@ -492,6 +492,12 @@ def test_parse_date_custom_format():
         ('03:30 PM', time(15, 30)),
         # test hour-only parsing
         ('4 pm', time(16, 0)),
+        # test 12 o'clock am/pm conversion: noon and midnight
+        ('12:00 pm', time(12, 0)),
+        ('12:00 PM', time(12, 0)),
+        ('12:30 am', time(0, 30)),
+        ('12 AM', time(0, 0)),
+        ('12:00:15 pm', time(12, 0, 15)),
     ],
 )
 def test_parse_time(input, expected):