Grid computing is the collection of computer resources from multiple locations to reach a common goal. According to the task publisher's computing power, we will classify the deceptive detection schemes into two categories, and then analyze the security of deceptive detection schemes based on the characteristics of computational task function. On the basis of double check, we proposed an improved scheme at the cost of time sacrifice called the secondary allocation scheme of double check. In our scheme, the security of double check has been greatly strengthened. Finally, we analyzed the common problem of High-Value Rare Events, improved the deceptive detection scheme due to [1], and then put forward a new deceptive detection scheme with better security and efficiency. This paper is revised and expanded version of a paper entitled "Deceptive Detection and Security Reinforcement in Grid Computing" [2] presented at 2013 5th International Conference on Intelligent Networking and Collaborative Systems, Xi'an city, Shanxi province, China, September 9-11, 2013.