We propose vehicular spread spectrum (SS) radar robust to mutual interference using zero correlation zone (ZCZ) code. SS radar schemes have been employed for vehicular radar systems due to their outstanding correlation property. However, this superiority is based on a premise that timing among codes is completely synchronized. In the practical driving environment, timing mismatch among radar signals is inevitable because the radar signals of several vehicles are independently transmitted at each different location and each timing and thus each radar signal is received at different timing. This timing offset is the main cause of orthogonality destruction among codes and thus radar signals from other vehicles become mutual interference. In order to solve this problem, we find out the new property of ZCZ code which maintains the complete orthogonality except to timing offset corresponding to chips (pulses) of multiple of 4 and employ ZCZ code to SS radar systems. Simulation results show the proposed scheme achieve better performance compared with the conventional SS radar scheme using pseudo code or gold code.