With the leader-follower formation pattern, a method for UAV formation rendezvous was developed based on the pursuit strategy. Firstly, the UAV non-decoupling 3D kinematics models were established by using the curve theory of differential geometry and the Frenet-Serret frames, where the curvature and the torsion were considered as the control effort. Secondly, the mathematical descriptions of the three-dimensional formation rendezvous were provided with the models, where the impact angular constraint in missile guidance was mapped to a flight path angle of the follower in formation rendezvous, and an additional azimuth angular constraint was introduced. Thirdly, the orientation deviation between the leader and the follower was measured by using an element of the special orthogonal group, and the element was mapped to a twist in an Lie algebra space corresponding to the Lie group by local coordinate mapping. Then, a geometric guidance law for formation rendezvous was developed by using the twist, and the corresponding curvature command and torsion command were presented. Finally, the numerical simulation for multi-UAVs formation rendezvous was carried out, under the leader flying straightly and making a turn, respectively. The simulation results show that the follower can track the orientation of the leader successfully and can converge to a specified configuration, which indicates that the proposed method is available.