diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml
index 661b2e5d05..d3be004436 100644
--- a/.github/workflows/deploy.yml
+++ b/.github/workflows/deploy.yml
@@ -134,8 +134,40 @@ jobs:
           python -m pip install cibuildwheel==2.2.2
       - name: Build wheels
         env:
-          CIBW_BEFORE_ALL: "yum install -y yum-utils wget && wget https://developer.download.nvidia.com/compute/cuda/10.1/Prod/local_installers/cuda-repo-rhel6-10-1-local-10.1.243-418.87.00-1.0-1.x86_64.rpm && rpm -i cuda-repo-rhel6-10-1-local-10.1.243-418.87.00-1.0-1.x86_64.rpm && yum clean all && yum -y install cuda-10-1 openblas-devel"
-          CIBW_SKIP: "*-manylinux_i686 pp* cp36* *musllinux*"
+          CIBW_BEFORE_ALL: "yum install -y yum-utils wget && wget -q https://developer.download.nvidia.com/compute/cuda/10.1/Prod/local_installers/cuda-repo-rhel6-10-1-local-10.1.243-418.87.00-1.0-1.x86_64.rpm && rpm -i cuda-repo-rhel6-10-1-local-10.1.243-418.87.00-1.0-1.x86_64.rpm && yum clean all && yum -y install cuda-10-1 openblas-devel"
+          CIBW_SKIP: "*-manylinux_i686 cp310* pp* cp36* *musllinux*"
+          CIBW_ENVIRONMENT: QISKIT_AER_PACKAGE_NAME=qiskit-aer-gpu AER_THRUST_BACKEND=CUDA CUDACXX=/usr/local/cuda/bin/nvcc
+        run: |
+          python -m cibuildwheel --output-dir wheelhouse
+      - uses: actions/upload-artifact@v2
+        with:
+          path: ./wheelhouse/*.whl
+      - name: Publish Wheels
+        env:
+          TWINE_PASSWORD: ${{ secrets.TWINE_PASSWORD }}
+          TWINE_USERNAME: qiskit
+        run : |
+          pip install -U twine
+          twine upload wheelhouse/*
+  gpu-build-310:
+    name: Build qiskit-aer-gpu wheels
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v2
+      - uses: actions/setup-python@v2
+        name: Install Python
+        with:
+          python-version: '3.7'
+      - name: Add msbuild to PATH
+        uses: microsoft/setup-msbuild@v1.0.2
+        if: runner.os == 'Windows'
+      - name: Install cibuildwheel
+        run: |
+          python -m pip install cibuildwheel==2.2.2
+      - name: Build wheels
+        env:
+          CIBW_BEFORE_ALL: "yum install -y yum-utils wget && wget -q https://developer.nvidia.com/compute/cuda/10.1/Prod/local_installers/cuda-repo-rhel7-10-1-local-10.1.105-418.39-1.0-1.x86_64.rpm && rpm -i cuda-repo-rhel7-10-1-local-10.1.105-418.39-1.0-1.x86_64.rpm && yum clean all && yum -y install cuda-10-1 openblas-devel"
+          CIBW_BUILD: "cp310-manylinux_x86_64"
           CIBW_ENVIRONMENT: QISKIT_AER_PACKAGE_NAME=qiskit-aer-gpu AER_THRUST_BACKEND=CUDA CUDACXX=/usr/local/cuda/bin/nvcc
         run: |
           python -m cibuildwheel --output-dir wheelhouse