Cross-selling emerges when complementary associations exist among products: A customer who has purchased a product may be willing to purchase another associated product with a certain probability; otherwise，the cross-selling opportunity of a stocked product can also dimish because of the shortage of its associated products． In this paper，a single-period multi-product centralized newsvendor model considering cross-selling and shortage penalty is formulated． The first-order necessary conditions and the upper and lower bounds of the optimal order quantity are given． For multiple newsvendors who make decisions individually and competitively，the newsvendor non-cooperative game of cross-selling product is modeled，which is proved supermodular．The first-order conditions，the uniqueness conditions and the bounds of the Nash equilibrium are developed．The difference between the decisions of the two models is presented and the analysis shows how the correlation of demand influences the expected profit． Finally，a computational study is conducted to observe the impacts of cross-selling，demand correlation，and shortage penalty on the order quantities and expected profits．