Due to the high demands of deep neural network (DNN) based applications on computational capability, it is hard for them to be directly run on mobile devices with limited resources. Computation offloading technology offers a feasible solution by offloading some computation-intensive tasks of neural network layers to edges or remote clouds that are equipped with sufficient resources. However, the offloading process might lead to excessive delays and thus seriously affect the user experience. To address this important problem, we first regard the average response time of multi-task parallel scheduling as our optimization goal. Next, the problem of computation offloading and task scheduling for DNN-based applications in cloud-edge computing is formulated with a scheme evaluation algorithm. Finally, the greedy and genetic algorithms based methods are proposed to solve the problem. The extensive experiments are conducted to demonstrate the effectiveness of the proposed methods for scheduling tasks of DNN-based applications in different cloud-edge environments. The results show that the proposed methods can obtain the near-optimal scheduling performance, and generate less average response time than traditional scheduling schemes. Moreover, the genetic algorithm leads to less average response time than the greedy algorithm, but the genetic algorithm needs more running time.INDEX TERMS Cloud-edge computing, DNN-based applications, computation offloading, task scheduling, greedy algorithm, genetic algorithm.