diff --git a/dev/tasks/gandiva-jars/travis.osx.yml b/dev/tasks/gandiva-jars/travis.osx.yml
index 3d5ea0b9117..e6675ffaf66 100644
--- a/dev/tasks/gandiva-jars/travis.osx.yml
+++ b/dev/tasks/gandiva-jars/travis.osx.yml
@@ -15,7 +15,7 @@
 # limitations under the License.
 
 os: osx
-osx_image: xcode8.3
+osx_image: xcode9.2
 sudo: required
 language: cpp
 compiler: clang
diff --git a/dev/tasks/homebrew-formulae/travis.osx.r.yml b/dev/tasks/homebrew-formulae/travis.osx.r.yml
index bc2f53dfb90..e9c2c9b3aed 100644
--- a/dev/tasks/homebrew-formulae/travis.osx.r.yml
+++ b/dev/tasks/homebrew-formulae/travis.osx.r.yml
@@ -15,6 +15,7 @@
 # limitations under the License.
 
 os: osx
+osx_image: xcode9.2
 language: r
 cache: packages
 r: {{ r_version }}
diff --git a/dev/tasks/homebrew-formulae/travis.osx.yml b/dev/tasks/homebrew-formulae/travis.osx.yml
index 8b23d7c767a..0fa84551ab6 100644
--- a/dev/tasks/homebrew-formulae/travis.osx.yml
+++ b/dev/tasks/homebrew-formulae/travis.osx.yml
@@ -15,6 +15,7 @@
 # limitations under the License.
 
 os: osx
+osx_image: xcode9.2
 language: ruby
 cache: bundler
 
diff --git a/dev/tasks/python-wheels/travis.osx.yml b/dev/tasks/python-wheels/travis.osx.yml
index ec3e97d2fe9..a489f54f05d 100644
--- a/dev/tasks/python-wheels/travis.osx.yml
+++ b/dev/tasks/python-wheels/travis.osx.yml
@@ -15,7 +15,7 @@
 # limitations under the License.
 
 os: osx
-osx_image: xcode8.3
+osx_image: xcode9.2
 language: generic
 
 # don't build twice
@@ -81,7 +81,7 @@ install:
   # move built wheels to a top level directory
   - mv -v arrow/python/dist/* dist/
   # reinstall openssl because travis' deployment script depends on it
-  - brew install openssl
+  - brew install openssl@1.1
 
 deploy:
   provider: releases