With the fast growing quantity of data generated by smart devices and the exponential surge of processing demand in the Internet of Things (IoT) era, the resource-rich cloud centers have been utilized to tackle these challenges. To relieve the burden on cloud centers, edge-cloud computation offloading becomes a promising solution since shortening the proximity between the data source and the computation by offloading computation tasks from the cloud to edge devices can improve performance and quality of service. Several optimization models of edge-cloud computation offloading have been proposed that take computation costs and heterogeneous communication costs into account. However, several important factors are not jointly considered, such as heterogeneities of tasks, load balancing among nodes and the profit yielded by computation tasks, which lead to the profit and cost-oriented computation offloading optimization model PECCO proposed in this article. Considering that the model is hard in nature and the optimization objective is not differentiable, we propose an improved Moth-flame optimizer PECCO-MFI which addresses some deficiencies of the original Moth-flame optimizer and integrate it under the edge-cloud environment. Comprehensive experiments are conducted to verify the superior performance of the proposed method when optimizing the proposed task offloading model under the edge-cloud environment.