diff --git a/stdlib/socket/0/tcp_server.rbs b/stdlib/socket/0/tcp_server.rbs
index 05f3d3f47..8dd6246d3 100644
--- a/stdlib/socket/0/tcp_server.rbs
+++ b/stdlib/socket/0/tcp_server.rbs
@@ -188,5 +188,5 @@ class TCPServer < TCPSocket
   # getaddrinfo() returns multiple addresses, TCPServer.new tries to create a
   # server socket for each address and returns first one that is successful.
   #
-  def initialize: (?String host, Integer port) -> untyped
+  def initialize: (?String? host, Integer | String port) -> void
 end
diff --git a/test/stdlib/socket/TCPServer_test.rb b/test/stdlib/socket/TCPServer_test.rb
new file mode 100644
index 000000000..b871b0d20
--- /dev/null
+++ b/test/stdlib/socket/TCPServer_test.rb
@@ -0,0 +1,37 @@
+require_relative "../test_helper"
+
+require "socket"
+
+class TCPServerSingletonTest < Test::Unit::TestCase
+  include TestHelper
+
+  library "socket"
+  testing "singleton(::TCPServer)"
+
+  def test_new
+    assert_send_type(
+      "(::Integer) -> ::TCPServer",
+      TCPServer, :new, 0
+    ).close
+
+    assert_send_type(
+      "(::String) -> ::TCPServer",
+      TCPServer, :new, "0"
+    ).close
+
+    assert_send_type(
+      "(::String, ::Integer) -> ::TCPServer",
+      TCPServer, :new, "127.0.0.1", 0
+    ).close
+
+    assert_send_type(
+      "(::String, ::String) -> ::TCPServer",
+      TCPServer, :new, "127.0.0.1", "0"
+    ).close
+
+    assert_send_type(
+      "(nil, ::Integer) -> ::TCPServer",
+      TCPServer, :new, nil, 0
+    ).close
+  end
+end