Recently, emerging approaches have been proposed to deal with robotic navigation problems, especially vision-and-language navigation task which is one of the most realistic indoor navigation challenge tasks. This task can be modelled as a sequential decision-making problem, which is suitable to be solved by deep reinforcement learning. Unfortunately, the observations provided from the simulator in this task are not fully observable states, which exacerbate the difficulty of implementing reinforcement learning. To deal with this challenge, this paper presents a novel method, called as attentive variational state tracker (AVAST), a variational approach to approximate belief state distribution for the construction of a reinforced navigator. The variational approach is introduced to improve generalization to the unseen environment which barely achieved by traditional deterministic state tracker. In order to stabilize the learning procedure, a fine-tuning process using policy optimization is proposed. From the experimental results, the proposed AVAST does improve the generalization relative to previous works in vision-and-language navigation task. A significant performance is achieved without requiring any additional exploration in the unseen environment.