In this paper, we consider the problem of enhancing the physical layer security of a wireless communication system by designing the optimal reflection coefficients of an intelligent reflecting surface (IRS) to maximize the secrecy rate of the system. In particular, we consider that a multi-antenna transmitter (Alice) is transmitting private messages to a single-antenna receiver (Bob), while a single-antenna eavesdropper (Eve) tries to intercept the message. Using an IRS comprising of multiple passive reflecting tiles, we formulate an unconstrained optimization framework to maximize the secrecy rate (SR) between the transmitter and the receiver as a function of the real-valued IRS phase shift coefficients. Thereafter, we propose a low-complexity Gradient Ascent (GA) based algorithm to solve this real-valued maximization problem. We numerically demonstrate that the performance of the proposed low-complexity optimization algorithm enjoys significant improvement over an existing state-of-the art technique in terms of the average SR and the computational complexity. Moreover, through simulation results, we show that in order to improve the SR, it is more effective to deploy a large number of IRS tiles rather than increasing the number of transmitting antennas.