This paper introduces a hybrid pilot-aided channel estimation technique for mitigating the effect of pilot contamination for the uplink of multi-cell multiuser massive MIMO systems. The proposed hybrid pilot is designed such that it enjoys the complementary advantages between time-multiplexed (TM) pilot and time-superimposed (TS) pilot and, thereby, allows superior solution to the conventional pilot schemes. We mathematically characterize the impact of hybrid pilot on the massive MIMO uplink by deriving a closed-form approximation for the uplink achievable rate. In the large-number-of-antennas regime, we obtain the asymptotically optimal solution for the hybrid pilot by jointly designing the TM pilot and the TS pilot. It is shown that either TM pilot or TS pilot has the advantages for large frame-size and limited frame-size transmission, respectively, while the hybrid pilot scheme can offer a superior performance to that employing either TM pilot or TS pilot. Numerical results demonstrate the effectiveness of the proposed design.