The invention belongs to the field of numerical control machining, and discloses a five-axis machining cutter axis feasibility map calculation method and system. The method comprises the following steps: using a binary image of a cutter axis feasibility map of a previous cutter contact point as an initial cutter axis feasibility map of a current cutter contact point, and calculating the boundary of the cutter axis feasibility map; carrying out collision detection on cutter axis directions in the boundary, setting pixel points corresponding to all the infeasible cutter axis directions as 0, updating the initial cutter axis feasibility map, and continuing to search for the boundary of the new cutter axis feasibility map until the cutter axis directions in the boundary are all feasible cutteraxis directions without collisions; outwardly extending the boundary of the finally updated target cutter axis feasibility map by a circle, and deducting the finally updated target cutter axis feasibility map by the cutter axis feasibility map before the extension to obtain an extended boundary; carrying out collision detection on the extended boundary, and adding feasible cutter axis directionsinto the target cutter axis feasibility map; and repeating the above operation after updating until cutter axis directions in the extended boundary are all infeasible cutter axis directions. The method and system disclosed by the invention has the advantages that the calculation load can be greatly reduced, and the calculation efficiency can be improved.