diff --git a/scripts/suppress_odbc.txt b/scripts/suppress_odbc.txt
new file mode 100644
index 00000000..e264f482
--- /dev/null
+++ b/scripts/suppress_odbc.txt
@@ -0,0 +1,6 @@
+# This is a suppression file for LeakSanitizer when running ODBC tests.
+
+# Unfortunately there is a leak from psqlodbca.so for which ASAN doesn't show
+# any stack at all, so we have no choice but to suppress all leaks from this
+# library, even though it could easily hide real problems.
+leak:psqlodbca.so
diff --git a/scripts/travis/script_odbc.sh b/scripts/travis/script_odbc.sh
index ec17822e..8ccc55f8 100755
--- a/scripts/travis/script_odbc.sh
+++ b/scripts/travis/script_odbc.sh
@@ -31,4 +31,4 @@ run_make
 
 # Exclude the tests which can't be run due to the absence of ODBC drivers (MS
 # SQL and MySQL).
-run_test -E 'soci_odbc_test_m.sql'
+LSAN_OPTIONS=suppressions=${TRAVIS_BUILD_DIR}/scripts/suppress_odbc.txt run_test -E 'soci_odbc_test_m.sql'