Broadcasting in Vehicular Ad Hoc Networks is the best way to spread emergency messages all over the network. With the dynamic nature of vehicular ad hoc networks, simple broadcast or flooding faces the problem called as Broadcast Storm Problem (BSP). The issue of the BSP will degrade the performance of a message broadcasting process like increased overhead, collision and dissemination delay. The paper is motivated to solve the problems in the existing Broadcast Strom Suppression Algorithms (BSSAs) like p-Persistence, TLO, VSPB, G-SAB and SIR. This paper proposes to suppress the B roadcast S torm P roblem and to improve the Emergency Safety message dissemination rate through a new BSSA based on S elective E pidemic B roadcast Algorithm (SEB). The simulation results clearly show that the SEB outperforms the existing algorithms in terms of ESM Delivery Ratio, Message Overhead, Collision Ratio, Broadcast Storm Ratio and Redundant Rebroadcast Ratio with decreased Dissemination Delay.