diff --git a/README.md b/README.md
index efd5e31..f9ab267 100644
--- a/README.md
+++ b/README.md
@@ -73,7 +73,7 @@ And the following IDEs/Compilers
 - GCC 4.8.4, 4.9.3, 5.3.0 and 6.1.1 (C++03, C++11, C++14, C++1z)
 - Clang 3.5 and 3.8
 - Xcode 8
-- Visual Studio Community 2017, and VS 2013 & 2015 (AppVeyor)
+- Visual Studio Community 2019, 2017, and VS 2013 & 2015 (AppVeyor)
 
 ### Dependencies
 
diff --git a/appveyor.yml b/appveyor.yml
index 3c1108e..14197ed 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -8,6 +8,7 @@ install:
   - git submodule update --init --recursive
  
 image:
+  - Visual Studio 2019
   - Visual Studio 2017
   - Visual Studio 2015
   - Visual Studio 2013
@@ -21,15 +22,15 @@ configuration:
 environment:
   matrix:
   - arch: Win32
-  - arch: Win64
+  - arch: x64
 
 init:
   - echo %APPVEYOR_BUILD_WORKER_IMAGE% - %configuration% - %arch%
   - if "%APPVEYOR_BUILD_WORKER_IMAGE%"=="Visual Studio 2017" (set vs=Visual Studio 15 2017)
   - if "%APPVEYOR_BUILD_WORKER_IMAGE%"=="Visual Studio 2015" (set vs=Visual Studio 14 2015)
-  - if "%APPVEYOR_BUILD_WORKER_IMAGE%"=="Visual Studio 2013" (set vs=Visual Studio 12 2013)
-  - if "%arch%"=="Win64" (set generator="%vs% Win64")
-  - if "%arch%"=="Win32" (set generator="%vs%")
+  - if "%arch%"=="x64" (set generator="%vs% Win64") else (set generator="%vs%")
+  # CMake uses a different grammar for Visual Studio 2019, with -A to specify architecture:
+  - if "%APPVEYOR_BUILD_WORKER_IMAGE%"=="Visual Studio 2019" (set generator="Visual Studio 16 2019" -A %arch%)
   - echo %generator%
  
 # scripts to run before build