In this brief, we investigate a finite-time output regulation (FTOR) problem for linear heterogeneous multi-agent systems (LHMAS). The objective is to design protocols such that each agent can follow the reference signal within a finite time. An exosystem is given to generate the reference signal and disturbances. Only a part of agents are assumed to have access to the system matrix and state of the exosystem. First, smooth distributed finite-time observers are designed to estimate them. Then, with the help of feedforward method, smooth state feedback and output feedback controllers are designed to address the FTOR problem. By virtue of the finite-time control method and the OR technique, it is shown that the proposed smooth distributed observers and controllers can achieve the finite-time convergence of the estimation errors and error outputs, respectively. Finally, a numerical example is presented for illustration.