diff --git a/internal/ceres/covariance_impl.cc b/internal/ceres/covariance_impl.cc
index 8c083fafa..0fa40ce87 100644
--- a/internal/ceres/covariance_impl.cc
+++ b/internal/ceres/covariance_impl.cc
@@ -337,7 +337,14 @@ bool CovarianceImpl::GetCovarianceMatrixInTangentOrAmbientSpace(
                  max_covariance_block_size]);
 
   bool success = true;
-#pragma omp parallel for num_threads(num_threads) schedule(dynamic) collapse(2)
+
+// The collapse() directive is only supported in OpenMP 3.0 and higher. OpenMP
+// 3.0 was released in May 2008 (hence the version number).
+#if _OPENMP >= 200805
+#  pragma omp parallel for num_threads(num_threads) schedule(dynamic) collapse(2)
+#else
+#  pragma omp parallel for num_threads(num_threads) schedule(dynamic)
+#endif
   for (int i = 0; i < parameters.size(); ++i) {
     for (int j = 0; j < parameters.size(); ++j) {
       // The second loop can't start from j = i for compatibility with OpenMP