This paper considers a new adaptive-critic optimal output regulation scheme for continuous-time general linear systems with unknown dynamics and unmeasurable disturbance. The objective of researching the optimal output regulation problem is pursuing the stability of the closed-loop system while enabling the output to optimally track the reference signal with disturbance rejection. The problem is solved by employing an approximate optimal regulator that consist of optimal feedback control obtained by a data-driven learning algorithm and optimal feedforward control achieved by solving regulator equation. The missing system matrices of the plant are exactly figured out by employing state/input data. Moreover, by employing the minimal polynomial of the exosystem matrix, the parameter of interference in the output equation is available. Then, a predefined cost function is presented based on the regulator equation that aims to design the optimal control law. The stability analysis demonstrate that the presented control scheme can stabilize the closed-loop system, meanwhile the output asymptotically tracks the reference signal. Finally, the effectiveness of the developed optimal control scheme is validated through an application towards the drum water level control of boiler-turbine systems.