Systematic Polar codes offers the same frame-error-rate (FER) performance compared with non-systematic Polar codes in almost communications channels although they have advantages in bit-error-rate (BER) performance. In recent papers, NAND flash memories have been confirmed for its asymmetric error characteristic, and the 2-Beta-Binomial (2-BBM) error model has been presented to provide accurate simulation of observed errors in multi-level cell (MLC) flash memories under different Program/Erase cycles. In this paper, we propose concatenating a distribution generator (DG) which can modify user data distribution with systematic Polar encoder (SPE) for MLC NAND Flash memory. The proposed method shows remarkable improvement in FER performances compared with non-systematic candidates, especially in lower pages of the two memory vendors.