The compliant peg-in-hole assembly method based on Attractive Region in Environment has achieved great performance in high-precision assembly for convex components. However, for nonconvex parts, there may be local minima in the constraint region, and jamming in the assembly process may arise by using the existing method. To solve the problem, this paper propose a compliant assembly method based on Attractive Region in Environment combined with geometric features. First, according to the geometric characteristics of the constraint region, sub-targets during the assembly process are designed. Then, low dimensional attractive regions are utilized to realize the phased directional movement and solve the jamming problem caused by the grooves. Furthermore, Impedance control is applied to guarantee the compliance of assembly. The experimental results of the nonconvex peg-in-hole assembly with clearance of 0.02 mm are presented and show the validity of the proposed method.