1. A lane determining device, comprising: a memory that stores road information including positions and forms of a first lane marking including a zebra zone and a deceleration zone and a second lane marking including solid lines or dashed lines existing on both sides of a lane; an imaging device that captures an image of the first lane marking and the second lane marking; and a controller configured to: obtain vehicle position information indicating a current position of a vehicle; based on the vehicle position information, access the stored road information including the positions and the forms of the lane markings around the current position of the vehicle; based on the accessed road information and without using the captured image, determine whether a branch point exists on the road in a forward direction of the vehicle; based on the accessed road information and without using the captured image, detects that the second lane marking does not exist at all before the branch point; wherein, if it is determined that the branch point does not exist on the road in the forward direction of the vehicle or it is detected that the second lane marking exists at all before the branch point, the controller: obtains image information of the captured image of the second lane marking; and determines a lane in which the vehicle is traveling based on the second lane marking in the image information and the road information, and if it is determined that the branch point exists on the road in the forward direction of the vehicle and it is detected that second lane marking does not exist at all before the branch point, the controller: obtains image information of the branch point including the captured image of the first lane marking; and determines a lane in which the vehicle is traveling after the branch point based on an imaging order of the first lane marking, a form of the first lane marking, a position of the first lane marking in the image information of the branch point, and the road information.