In　many　flexible　manufacturing　systems,　it　is　quite　important　to　balance　the　number　of　jobs　allocated　to　each　single　production　facility.　Yang,　Ye　and　Zhang　(2003)　considered　the　problem　that　schedules　n　jobs　on　two　identical　parallel　machines,　with　a　capacity　constraint　on　each　machine,　i.e.　the　number　of　jobs　that　each　machine　can　process　is　bounded,　so　as　to　minimize　the　total　weighted　completion　time　of　these　jobs　by　semidefinite　programming　relaxation.　In　this　paper,　we　further　consider　the　problem　of　three　identical　parallel　machines　with　capacity　constraints　and　present　a　1.4446-approximation　algorithm　based　on　complex　semidefinite　programming　relaxation　by　extending　the　previous　techniques.　©　2020,　Springer　Nature　Switzerland　AG.