The problem of path planning in unknown environments remains a challenging problem - as the environment is gradually observed during the navigation, the underlying planner has to update the environment representation and replan, promptly and constantly, to account for the new observations. In this paper, we present a visibility graph-based planning framework capable of dealing with navigation tasks in both known and unknown environments. The planner employs a polygonal representation of the environment and constructs the representation by extracting edge points around obstacles to form enclosed polygons. With that, the method dynamically updates a global visibility graph using a two-layered data structure, expanding the visibility edges along with the navigation and removing edges that become occluded by newly observed obstacles. When navigating in unknown environments, the method is attemptable in discovering a way to the goal by picking up the environment layout on the fly, updating the visibility graph, and fast re-planning corresponding to the newly observed environment. We evaluate the method in simulated and real-world settings. The method shows the capability to attempt and navigate through unknown environments, reducing the travel time by up to 12-47% from search-based methods: A*, D* Lite, and more than 24-35% than sampling-based methods: RRT*, BIT*, and SPARS.