diff --git a/pkg/compose/containers.go b/pkg/compose/containers.go
index 3cbd1c13d..af05915db 100644
--- a/pkg/compose/containers.go
+++ b/pkg/compose/containers.go
@@ -99,6 +99,12 @@ func isService(services ...string) containerPredicate {
 	}
 }
 
+func isRunning() containerPredicate {
+	return func(c moby.Container) bool {
+		return c.State == "running"
+	}
+}
+
 func isNotService(services ...string) containerPredicate {
 	return func(c moby.Container) bool {
 		service := c.Labels[api.ServiceLabel]
diff --git a/pkg/compose/logs.go b/pkg/compose/logs.go
index 7fdf15e32..18d0e2114 100644
--- a/pkg/compose/logs.go
+++ b/pkg/compose/logs.go
@@ -72,6 +72,7 @@ func (s *composeService) Logs(
 	}
 
 	if options.Follow {
+		containers = containers.filter(isRunning())
 		printer := newLogPrinter(consumer)
 		eg.Go(func() error {
 			_, err := printer.Run(false, "", nil)