We consider a distributed computing scenario in which a master wants to perform matrix multiplication of two confidential inputs with multiple workers in parallel. In such a setting, a master does not want to reveal information about two input matrices to workers in an information-theoretic sense. We propose a secure distributed computing scheme that can efficiently cope with straggling effects by applying polynomial codes on sub-tasks assigned to workers. The achievable recovery threshold, i.e., the number of workers that a master needs to wait for to get the final product, of our proposed scheme is revealed to be order-optimal to the number of workers, which proves the scalability of our scheme. It is shown that our scheme can reduce waiting time at the master by mitigating straggling effects.