Terahertz(THz) multiuser massive multiple-input multiple-output(MIMO) has been envisioned as a promising technique to support massive connectivity in next-generation wireless networks. However,due to ultra-high frequency band, the path attenuation of THz channels is extremely severe, resulting in limited wireless coverage. In this paper, we propose an intelligent reflecting surface(IRS)-assisted THz multiuser massive MIMO technique to enhance coverage. First, we design an IRS-assisted THz communication framework with a low-cost sub-connected hybrid precoding architecture, including uplink data transmission and downlink data transmission. In particular, precoding errors due to the limitations of physical devices and environments are taken into consideration. Then, we derive the closed-form expressions for uplink and downlink spectral efficiencies, and reveal the impacts of system parameters. Finally, we conduct extensive simulations to verify the effectiveness of the proposed IRS-assisted THz multiuser massive MIMO technique.