We investigate the physical layer security for multiple-input single-output (MISO) multigroup multicast system in the presence of multiple eavesdroppers (Eves). To elaborate, we aim to tackle the secrecy rate maximization (SRM) problem of the multicast system by proposing an algorithm for secure beam-forming. Here, we adopt the concept of artificial noise (AN) which is used for disturbing Eves by sending noise deliberately. Thus, we simultaneously design beamforming vectors and AN vector to maximize the secrecy rate of the system. We formulate the SRM problem in the form of non-convex max-min fair problem which is hard to solve due to its non-convexity. Therefore, in order to tackle this problem, we first reformulate this SRM problem to epigraph form, and we utilize the minorization maximization (MM) algorithm and rank-1 reduction technique. Simulation results show that our proposed algorithm improves the secrecy rate of given system model and outperforms the conventional algorithm for secure beamforming.