This letter investigates covert communication in an intelligent reflecting surface (IRS)-assisted system. We propose a novel algorithm that jointly optimizes the transmission probability, transmit power at a transmitter, and the reflection matrix of an IRS with the goal of maximizing the achievable rate at a receiver while ensuring the covertness of the transmission. We first analyze the expected detection error probability at a warden, and then develop a technique for covert rate maximization using only one-dimensional search methods. The proposed strategy achieves near-optimal performance and its performance is superior to that of the conventional scheme with a fixed transmission probability.