Future smart grid (SG) has been considered a complex and advanced power system, where energy consumers are connected not only to the traditional energy retailers (e.g., the utility companies), but also to some local energy networks for bidirectional energy trading opportunities. This paper aims to investigate a hybrid energy trading market that is comprised of an external utility company and a local trading market managed by a local trading center (LTC). The existence of local energy market provides new opportunities for the energy consumers and the distributed energy sellers to perform the local energy trading in a cooperative manner such that they all can benefit. This paper first quantifies the respective benefits of the energy consumers and the sellers from the local trading and then investigates how they can optimize their benefits by controlling their energy scheduling in response to the LTC's pricing. Two different types of the LTC are considered: 1) the nonprofit-oriented LTC, which solely aims at benefiting the energy consumers and the sellers; and 2) the profit-oriented LTC, which aims at maximizing its own profit while guaranteeing the required benefit for each consumer and seller. For each type of the LTC, the optimal trading problem is formulated and the associated algorithm is further proposed to efficiently find the LTC's optimal price, as well as the optimal energy scheduling for each consumer and seller. Numerical results are provided to validate the benefits of the hybrid energy trading market and the performance of the proposed algorithms.