Since each user's demodulation reference signals are superimposed and interfere with each other in the case where multiple users simultaneously transmit signals at the same frequency, it is difficult to accurately estimate the channel impulse response for each user. In this paper, a special signal matrix is designed for the transmission format 4 of the 5G system Physical Uplink Control Channel (PUCCH) by using the characteristics of demodulation reference signals of different users. Then we combine this signal matrix with traditional single-user channel estimation algorithms to propose three channel estimation algorithms including Least Squares (LS)-based spline interpolation, LS-based Discrete Cosine Transform (DCT) interpolation algorithm, and Liner Minimum Mean Squared Error (LMMSE)-based DCT interpolation algorithm. Finally, the scenes of two users and four users are simulated. The simulation results show that three proposed channel estimation algorithms are applicable to the format 4 of 5G system PUCCH, which has great reference value for engineering applications.