This paper considers an intelligent reflecting surface (IRS)-assisted covert communication system, where an IRS is deployed for the covert transmission from a legitimate transmitter (Alice) to a legitimate receiver (Bob) with the presence of an eavesdropper (Willie). Since Willie is not a legitimate communication node and cannot control the IRS's reflection, it has uncertainty about the channel information of the Alice-IRS and IRS-Willie links. Meanwhile, Willie also has uncertainty about its noise power. Having such channel and noise information uncertainties, Willie finds an optimal power detection threshold to minimize its false detection probability. Under this system setup, we investigate maximizing the covert rate of the legitimate communication from Alice to Bob, by jointly optimizing Alice's transmit power and the IRS's reflecting phase shifts. We have proposed two efficient joint optimization algorithms for the continuous and discrete IRS reflecting phase shift cases, respectively. The proposed algorithm for the previous case is based on the semidefinite relaxation technique, and that for the latter case is based on the alternating optimization technique. Simulation results have demonstrated the superiority and necessity of jointly optimizing the transmit power and IRS reflecting phase shifts on improving the covert rate performance, as compared to other benchmark schemes.