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Many applications of wireless sensor network use a mobile sink to collect data detected by network nodes. To make routing approach in such scenarios better support sink mobility and be adaptive to varying network conditions, an adaptive routing approach based on reinforcement learning was proposed. A comprehensive reward function concerning mean hop count, residual energy and link quality was designed for learning to achieve a trade-off among multiple metrics of the network performance. Sink announcement was used to guarantee the convergence speed for obtaining an optimal route. Theoretical analysis shows that the approach is feasible for resources constrained sensor nodes due to its low overhead, small storage and computation requirements. Simulation results show the feasibility and superiority of the proposed approach.