Space limitation and multi-antenna channel acquisition prevent Massive multiple-input multiple-output (MIMO) from being easily deployed. The use of multi-polarized antennas can be one solution to alleviate the first obstacle. Furthermore, the dual structured precoding, in which a preprocessing based on the spatial correlation and a subsequent linear precoding based on the short-term channel state information at the transmitter (CSIT) are concatenated, can reduce the feedback overhead efficiently. To reduce the feedback overhead further, we propose a dual structured multi-user linear precoding, in which the subgrouping method based on co-polarization is additionally applied to the spatially grouped mobile stations (MSs) in the preprocessing stage. By investigating the behavior of the asymptotic performance as a function of the cross-polar discrimination (XPD) parameter, we also propose a new dual structured precoding, in which the XPD, spatial correlation, and CSIT quality are jointly utilized in the precoding/feedback for the multi-polarized multi-user massive MIMO system.