In Vehicle-to-Everything (V2X) communication, the high mobility of vehicles generates the Doppler shift which leads to channel uncertainties. Moreover, the reasons for channel uncertainties also include the finite channel feedback, channels state information (CSI) loss and latency. With this concern, we formulate a joint spectrum and power allocation problem for V2X communication with imperfect CSI. Specifically, the sum capacity of cellular user equipments (CUEs) is maximized subject to the minimum Signal-to-Interference-and-Noise Ratio (SINR) requirements of CUEs and the outage probability constraints of vehicular user equipments (VUEs). Then, two different robust resource allocation approaches are designed to solve the problem. One is Bernstein Approximation-based Robust Resource Allocation approach. More specifically, Bernstein approximations are employed to convert the chance constraint into a calculable constraint, and Bisection search method is proposed to obtain the optimal allocation solution with low complexity. Then, for further reducing the computational complexity, Self-learning Robust Resource Allocation approach, which includes a learning method and an analytical mapping method, is proposed as the second approach. The learning method is devised to learn the uncertainty set which transforms the chance constraint into calculable constraints, and the analytical mapping method is proposed to obtain closed-form solutions of the resource allocation problem. Finally, the simulation results prove that the proposed approaches can improve the capacity of all CUEs effectively whilst ensuring the reliability of the channel.