With the development of high speed trains (HST) in many countries, providing broadband wireless services in HSTs is becoming crucial. Orthogonal frequency-division multiplexing (OFDM) has been widely adopted for broadband wireless communications due to its high spectral efficiency. However, OFDM is sensitive to the time selectivity caused by high-mobility channels, which costs large spectrum or time resources to obtain the accurate channel state information (CSI). Therefore, the channel estimation in high-mobility OFDM systems has been a long-standing challenge. In this paper, we first propose a new position-based high-mobility channel model,in which the HST's position information and Doppler shift are utilized to determine the positions of the dominant channel coefficients. %In this way, we can reduce the estimation complexity and to design the transmitted pilot.Then, we propose a joint pilot placement and pilot symbol design algorithm for compressed channel estimation. It aims to reduce the coherence between the pilot signal and the proposed channel model, and hence can improve the channel estimation accuracy. Simulation results demonstrate that the proposed method achieves better performances than existing channel estimation methods over high-mobility channels. Furthermore, we give an example of the designed pilot codebook to show the practical applicability of the proposed scheme.