In this work, an Intelligent Reflecting Surface (IRS) aided and Artificial Noise (AN) enhanced covert wireless communications is considered to improve the covert transmission performance. Firstly, the detection performance at Willie is analyzed and a lower bound on Willie’s minimum total detection error probability is presented. On this basis, an optimization problem that maximizes the effective throughput subject to the covertness constraint and the maximum AN transmit power constraint is formulated. The optimization problem is non-convex, which is generally difficult to tackle directly. Then, an alternating iterative algorithm based on Dinkelbach method is proposed to jointly design the IRS reflection beamforming and Alice’s transmit power together with Bob’s AN transmit power. In order to reduce the computational complexity, a low-complexity algorithm is further proposed to obtain analytical expressions for the corresponding optimization variables. Simulation results show that the proposed scheme improves significantly the covert transmission performance compared with the schemes without IRS and without AN.