This paper considers a secure multigroup multicast multiple-input single-output (MISO) com-munication system aided by an intelligent reflecting surface (IRS). Specifically, we aim to minimize the transmit power at Alice via jointly optimizing the transmit beamformer, artificial noise (AN) vector and phase shifts at the IRS subject to the secrecy rate constraints as well as the unit modulus constraints of IRS phase shifts. To tackle the optimization prob-lem, we first transform it into a semidefinite relax-ation (SDR) problem, and then alternately update the transmit beamformer and AN matrix as well as the phase shifts at the IRS. In order to reduce the high computational complexity, we further propose a low-complexity algorithm based on second-order cone programming (SOCP). We decouple the optimization problem into two sub-problems and optimize the trans-mit beamformer, AN vector and the phase shifts al-ternately by solving two corresponding SOCP sub-problem. Simulation results show that the proposed SDR and SOCP schemes require half or less transmit power than the scheme without IRS, which demon-strates the advantages of introducing IRS and the ef-fectiveness of the proposed methods.