The task of vision-and-language navigation in continuous environments (VLN-CE) aims at training an autonomous agent to perform low-level actions to navigate through 3D continuous surroundings using visual observations and language instructions. The significant potential of VLN-CE for mobile robots has been demonstrated across a large number of studies. However, most existing works in VLN-CE focus primarily on transferring the standard discrete vision-and-language navigation (VLN) methods to continuous environments, overlooking the problem of collisions. Such oversight often results in the agent deviating from the planned path or, in severe instances, the agent being trapped in obstacle areas and failing the navigational task. To address the above-mentioned issues, this paper investigates various collision scenarios within VLN-CE and proposes a classification method to predicate the underlying causes of collisions. Furthermore, a new VLN-CE algorithm, named Safe-VLN, is proposed to bolster collision avoidance capabilities including two key components, i.e., a waypoint predictor and a navigator. In particular, the waypoint predictor leverages a simulated 2D LiDAR occupancy mask to prevent the predicted waypoints from being situated in obstacle-ridden areas. The navigator, on the other hand, employs the strategy of `re-selection after collision' to prevent the robot agent from becoming ensnared in a cycle of perpetual collisions. The proposed Safe-VLN is evaluated on the R2R-CE, the results of which demonstrate an enhanced navigational performance and a statistically significant reduction in collision incidences.