The reaction of pp → pK+Λ is a very good channel to study N* resonances through their KΛ decay mode, because there is no mixing of isospin Ⅰ = 1/2 and Ⅰ = 3/2 due to isospin conservation. In this work, we extend a resonance model, which can reproduce the total cross section very well, to offer differential cross section information about this reaction. It can serve as a reference to build the scheduled hadron detector at Lanzhou Cooler Storage Ring (CSR). Experiment measurement of these differential cross sections in the future will supply us more constraints on the model and help us understanding the strangeness production dynamics better.