Developing non-terrestrial networks (NTN) in future wireless networks has been widely recognized to bring advanced communication services to remote and unserved areas. The Low-Earth-Orbit (LEO) constellation has emerged as a promising component for NTN to provide seamless and fast global connectivity. However, since natural dynamic features, the mobility management, in particular the handover (HO) between satellites, plays an important role in ensuring a stable and continuous data service for NTN. Motivated by this fact, this paper proposes a HO optimization strategy based on conditional handover (CHO) mechanism to enhance service continuity in LEO-based NTN. A reward function, related to link service time and service capability, is firstly designed to modify the monitoring conditions of target satellite candidates. The optimal target selection algorithm is proposed to obtain the maximum reward for each CHO. Then, a service continuity performance graph (SCG) model is constructed to predict different potential CHO combinations in service duration. On the basis of SCG, the HO sequence supporting a high-quality and stable data service is predictively calculated for each accessing user. Simulation results demonstrate that the proposed HO optimization scheme can obviously reduce handover rate under different NTN conditions and can better enhance NTN service continuity.