diff --git a/neovim/postinstall b/neovim/postinstall
index 6e15a37..c441985 100755
--- a/neovim/postinstall
+++ b/neovim/postinstall
@@ -2,5 +2,19 @@
 
 set -exuo pipefail
 
-[ -d ~/.virtualenvs/neovim3 ] || python3 -m venv ~/.virtualenvs/neovim3
-~/.virtualenvs/neovim3/bin/python -c 'import pynvim' || ~/.virtualenvs/neovim3/bin/pip install pynvim
+VENV="~/.virtualenvs/neovim3"
+PYTHON="${VENV}/bin/python"
+
+if [ -d "${VENV}" ]; then
+    # Upgrade the venv if the global Python version has changed.
+    local_py=$("${PYTHON}" --version)
+    global_py=$(python3 --version)
+    if [ "${local_py}" != "${global_py}" ]; then
+        python3 -m venv --upgrade "${VENV}"
+        "${PYTHON}" -m pip install --upgrade pip
+    fi
+else
+    python3 -m venv "${VENV}"
+fi
+
+"${PYTHON}" -c 'import pynvim' || "${PYTHON}" -m pip install pynvim