Despite its potential for reducing the detection probability at the warden, the effectiveness of covert communication in practical situations is often hindered by harsh wireless signal propagation environments. Fortunately, intelligent reflecting surface (IRS) can establish programmable wireless channels to tackle this issue. In this paper, we propose two IRS-assisted finite-blocklength covert communication schemes to maximize the effective covert throughput (ECT) with equal and unequal transmit prior probabilities, respectively. First, we analyze the warden’s detection performance with its optimal detection threshold derived, which is the worst situation for the covert transmission. We jointly optimize the transmit power, transmission blocklength, prior transmission probability and IRS’s phase shifts to maximize ECT in the common scenario and packet-generation scenario, respectively, which covers a wide range of practical applications. The designed optimal phase shifts not only maximize the signal-to-noise ratio at the receiver, but also introduce uncertainty to the warden for covertness provisioning. The closed-form expressions of solutions indicate that there exists a non-trivial trade-off between ECT and covertness, and adopting unequal transmit prior probabilities is proved to perform better than its counterpart of equal probabilities. Finally, numerical results demonstrate the superior performance achieved by the proposed covert communication schemes.