This paper studies first-price auction with asymmetric risk preferences firstly in a model with independent private values. Based on the independent identically distributed (IID) hypothesis, we analyze two kinds of situations, the strong and weak risk aversion, and find that:1) A first-price auction with asymmetric risk preferences has a monotonic equilibrium and the strong bidder bids more aggressively than the weak bidder. 2) With symmetric risk preferences, the first-price auction has a symmetric equilibrium and bidders bid more aggressively when their risk aversion are strong. 3) In the first-price auction with symmetric and asymmetric risk preferences, we sort the strong bidders' and the weak bidders' bidding strategies. 4) A first-price auction with asymmetric risk preferences may preclude allocative efficiency while the auction with symmetric risk preferences allocates efficiently.