Polar codes are the first coding schemes that probably achieve the Shannon capacity of memory-less symmetric channels with an explicit construction based on the channel polarization. Moreover, polar codes are adopted for control channels in the fifth generation mobile communication systems (5G). Here, the basic principle of polar codes is briefly introduced, including polar encoding and decoding. Furthermore, a concatenated coding scheme of polar codes and parity-check codes, called the parity-check-concatenated (PCC) polar codes is proposed. The information bits are encoded by an outer parity-check encoder and an inner polar encoder. At the receiver, the parity-check-aided successive cancellation list (PC-aided SCL) algorithm is applied for decoding. Simulation results show that PCC polar codes could have evident performance gains over the cyclic redundancy check-concatenated polar codes without increasing the complexity of encoding and decoding. Therefore, PCC polar codes could meet the requirements of 5G for the error correction performance.