In smart homes, the computational offloading technology of edge cloud computing (ECC) can effectively deal with the large amount of computation generated by smart devices. In this paper, we propose a computational offloading strategy for minimizing delay based on the back-pressure algorithm (BMDCO) to get the offloading decision and the number of tasks that can be offloaded. Specifically, we first construct a system with multiple local smart device task queues and multiple edge processor task queues. Then, we formulate an offloading strategy to minimize the queue length of tasks in each time slot by minimizing the Lyapunov drift optimization problem, so as to realize the stability of queues and improve the offloading performance. In addition, we give a theoretical analysis on the stability of the BMDCO algorithm by deducing the upper bound of all queues in this system. The simulation results show the stability of the proposed algorithm, and demonstrate that the BMDCO algorithm is superior to other alternatives. Compared with other algorithms, this algorithm can effectively reduce the computation delay.