We investigate a non-orthogonal pilot design for massive multiple-input multiple-output (MIMO) channel estimation with orthogonal frequency division multiplexing (OFDM) modulation. Leveraging two-dimensional (2D) beam based channel model, we formulate a signal model for channel estimation with a comb-type pilot structure. Then, we propose generalized phase shift pilots (GPSPs) and reveal that both GPSPs and their discrete Fourier transform (DFT) have constant modulus, and the DFT of GPSPs also has optimal autocorrelation property and beneficial crosscorrelation property. Subsequently, we prove that the inter-user interference with GPSPs is negligible when the weight sequence length of GPSPs is large enough or when channels can be differentiated in the angle domain, validating the feasibility of GPSPs, especially when the statistical channel state information (CSI) is unavailable. Further, by leveraging the correlation properties of GPSPs, an efficient implementation for GAMP based channel estimation is provided. Simulation results indicate that GPSPs enable low-complexity channel estimation while ensuring satisfactory performance.