Abstract: The resolve solution to the expected net present value equation of a kind of Markov model（Pfeifer model），in infinite horizon purchasing cases，is given，in order to make easer to the study and analysis of such problem.Such model is always used in the study on Customer Relationship Management（CRM） problem.Based on the matrix inverse formula，the inverse matrix is decomposed and simplified，its resolve solution is computed，and the resolve solution for the expected net present value vector for such kind of Markov model V=（I-P）^-1R is found，then the solution suited for the n order case is expended.Based on the computed result，a short further analysis and discussion to its CLV（the total expected net present value in customer life cycle） is made.The resolve solution to the expected net present value will supply an easy study base to such kind of problem analysis.