Coding distributed computing (CDC) has been widely used in many fields, such as recommendation systems, image classification, etc.. In the process of applying CDC to the recommendation systems, the user's privacy protection and stragglers (computation latency) should be taken into consideration. Although many solutions have been proposed to address these two considerations, they require additional computation resources that may result in higher communication load. In this paper, we propose PCRec, a Private Coding computation scheme based on edge computing, which solves the problem of the stragglers and the privacy protection in Recommendation systems and further reduces the communication load. Specifically, PCRec aims to protect the privacy and mitigate the impact of the stragglers by utilizing the coding method and obfuscating the data involved in the calculation. Secondly, PCRec uses specific task allocation scheme and coding computation scheme to further reduce the communication load. To evaluate the performance of PCRec, we compare the PCRec with the three related schemes, such as PCMM, PC, UNMDS, in terms of communication load and computation latency. The experimental results demonstrate that the PCRec scheme can reduce the communication load up to 50% and the computation latency by at least 39% compared with other schemes. Therefore, PCRec not only protects the user's privacy and mitigates the impact of stragglers, but also reduces the communication load efficiently.