As a reaction and complement to cloud computing, edge computing is a computing paradigm designed for low-latency computing. Edge servers, deployed at the boundary of the Internet, bridge those distributed end devices and the centralized cloud server, forming a harmonic architecture with low latency and balanced loadings. Elaborated task scheduling, including task assignment and processor dispatching, is essential to the success of edge computing systems in dense small cell networks. Plenty of issues need to be considered, such as servers’ computing power, storage capacity, loadings, bandwidth and tasks’ sizes, delays, partitionability, etc. This study contributes to the task scheduling for multicore edge computing environments. We first show that this scheduling problem is an NP -hard problem. An efficient and effective heuristic is then proposed to tackle the problem. Our Multicore Task assignment for maximum Rewards (MAR) scheme differs from most previous schemes in jointly considering all three critical factors: namely task partitionability, multicore, and task properties. A task’s priority is decided by its cost function, which takes into account the task’s size, deadline, partitionability, cores’ loadings, processing power, and so forth. First, tasks from end devices are assigned to edge servers considering servers’ loadings and storage. Next, tasks are assigned to the cores of the selected server. Simulations compare the proposed scheme with First-Come-First-Serve (FCFS), Shortest Task First (STF), Delay Priority Scheduling (DPS), and Green Greedy Algorithm (GGA). Simulations demonstrate that the task completion ratio can be significantly increased, and the number of aborted tasks can be greatly reduced. Compared with FCFS (First-Come-First-Serve), STF (Shortest Task First), DPS (Delay Priority Scheduling), and GGA (Green Greedy Algorithm), the improvement in task completion ratio for hotspots is up to 26%, 25%, 22%, and 9%, respectively.