In Kernel Space, Support Vectors selection is an important issue for Support Vector Machines (SVMs). But, at present most sample selection methods have a common disadvantage that the candidate set for Support Vectors is the whole sample space, so, it may select interior samples or ldquooutliersrdquo that have little or even bad effect on the classifying quality. To tackle it, two improved methods based on effective candidate set are proposed in the paper. By using these two methods, the effective candidate set is firstly identified through ldquoremoving centerrdquo and eliminating ldquooutlinersrdquo, and then Support Vectors are selected in this effective candidate set. Experimental results show that the methods reserved effective candidate samples undoubtedly, and also improved the performance of the SVMs classifier in kernel space.