This paper addresses a straight-line finite-time path following cooperative control problem for multiple underactuated surface vessels(USVs) subjected to surge velocity and yaw angle constraints. Aiming at the navigation environment of USVs, we consider the matched and mismatched disturbances which are estimated and compensated by introducing the integral line-of-sight guidance law and finite-time observer in the control scheme. An asymmetric barrier Lyapunov function is designed to ensure the constraints are not violated during USV's navigation. Then a finite-time controller is constructed via adding a power integrator to guarantee that the system error can converge to zero within finite time. Finally, the simulation results further show the effectiveness of the proposed method.