In this study, we propose a novel method for a travel path inference problem from sparse GPS trajectory data. This problem involves localization of GPS samples on a road network and reconstruction of the path that a driver might have been following from a low rate of sampled GPS observations. Particularly, we model travel path inference as an optimization problem in both the spatial and temporal domains and propose a novel hybrid hidden Markov model (HMM) that uses a uniform cost search (UCS)-like novel combinational algorithm. We provide the following improvements over the previous studies that use HMM-based methods: (1) for travel path inference between matched GPS positions, the proposed hybrid HMM algorithm evaluates all candidate paths to find the most likely path for both the temporal and spatial domains. In contrast, previous studies either create interpolated trajectories or connect matched GPS positions using the shortest path assumption, which might not be true, especially in urban road networks (Goh et al. 2012; Lou et al. 2009). (2) The proposed algorithm uses legal speed limits for the evaluation of discrepancy in the temporal domain as in Goh et al. (2012), and Lou et al. (2009) only if there is not sufficient historical average speed data; otherwise, we use historical average speed computed from data. Our experiments with real datasets show that our algorithm performs better than the state of the art VTrack algorithm (Thiagarajan et al. 2009), especially for cases where GPS data is sampled infrequently.