VANET is a hybrid ad-hoc network between vehicles and road side units. Due to the high mobility of nodes, to find a stable data communication route in VANET is an open challenge. This paper introduces a new hybrid routing algorithm to find a stable route by using zone-based routing (ZBR), fuzzy logic, and NIBC algorithm. In proposed algorithm ZBR is used to divide the network into small and stable zones, fuzzy logic is used to find the quality of links between nodes, and NIBC to find the stable route in short time. Six techniques for the VANET has been implemented and compared in this paper. NS2.34 network simulator is used for simulations. Simulations were carried out for variable transmission rate and variable speed. Five performance parameters have been taken to analyse the results. Simulation results have shown that NIBC algorithms improve the performance of VANET.