diff --git a/sdk/core/azure-core/CHANGELOG.md b/sdk/core/azure-core/CHANGELOG.md
index 373ea4ab64..1fb18874e5 100644
--- a/sdk/core/azure-core/CHANGELOG.md
+++ b/sdk/core/azure-core/CHANGELOG.md
@@ -8,6 +8,8 @@
 
 ### Bugs Fixed
 
+- [[#5130]](https://github.com/Azure/azure-sdk-for-cpp/issues/5130) `Url::AppendPath()` and `Url::SetPath()` may end up with a double slash at the beginning of a path.
+
 ### Other Changes
 
 ## 1.11.0-beta.2 (2023-11-02)
diff --git a/sdk/core/azure-core/src/http/url.cpp b/sdk/core/azure-core/src/http/url.cpp
index a46c013c3b..e9c3228f14 100644
--- a/sdk/core/azure-core/src/http/url.cpp
+++ b/sdk/core/azure-core/src/http/url.cpp
@@ -219,7 +219,10 @@ std::string Url::GetUrlWithoutQuery(bool relative) const
   {
     if (!relative)
     {
-      url += "/";
+      if (m_encodedPath.empty() || m_encodedPath[0] != '/')
+      {
+        url += "/";
+      }
     }
 
     url += m_encodedPath;
diff --git a/sdk/core/azure-core/test/ut/url_test.cpp b/sdk/core/azure-core/test/ut/url_test.cpp
index 64218ecab4..de3d4d833d 100644
--- a/sdk/core/azure-core/test/ut/url_test.cpp
+++ b/sdk/core/azure-core/test/ut/url_test.cpp
@@ -333,4 +333,49 @@ namespace Azure { namespace Core { namespace Test {
     EXPECT_NE(params.find("param"), params.end());
     EXPECT_EQ(params["param"], "value");
   }
+
+  TEST(URL, LeadingSlashInPath)
+  {
+    Core::Url const u0("https://www.microsoft.com");
+    Core::Url const u1("https://www.microsoft.com/");
+
+    EXPECT_EQ(u0.GetAbsoluteUrl(), "https://www.microsoft.com");
+    EXPECT_EQ(u1.GetAbsoluteUrl(), "https://www.microsoft.com");
+
+    {
+      auto url0 = u0;
+      auto url1 = u1;
+      url0.AppendPath("path");
+      url1.AppendPath("path");
+      EXPECT_EQ(url0.GetAbsoluteUrl(), "https://www.microsoft.com/path");
+      EXPECT_EQ(url1.GetAbsoluteUrl(), "https://www.microsoft.com/path");
+    }
+
+    {
+      auto url0 = u0;
+      auto url1 = u1;
+      url0.AppendPath("/path");
+      url1.AppendPath("/path");
+      EXPECT_EQ(url0.GetAbsoluteUrl(), "https://www.microsoft.com/path");
+      EXPECT_EQ(url1.GetAbsoluteUrl(), "https://www.microsoft.com/path");
+    }
+
+    {
+      auto url0 = u0;
+      auto url1 = u1;
+      url0.SetPath("path");
+      url1.SetPath("path");
+      EXPECT_EQ(url0.GetAbsoluteUrl(), "https://www.microsoft.com/path");
+      EXPECT_EQ(url1.GetAbsoluteUrl(), "https://www.microsoft.com/path");
+    }
+
+    {
+      auto url0 = u0;
+      auto url1 = u1;
+      url0.SetPath("/path");
+      url1.SetPath("/path");
+      EXPECT_EQ(url0.GetAbsoluteUrl(), "https://www.microsoft.com/path");
+      EXPECT_EQ(url1.GetAbsoluteUrl(), "https://www.microsoft.com/path");
+    }
+  }
 }}} // namespace Azure::Core::Test