A pressure vessel is disclosed comprising an inner vessel with a rotationally symmetrical middle part with an axis of symmetry along the middle part and two dome-shaped polar caps which close off the middle part, and an outer layer, wound on the inner vessel to reinforce it, made of fiber composite material made of a plurality of plies of fibers embedded in a matrix material which are arranged one above another, which run as a fiber band made of a number of fibers with a location-dependent and position-dependent fiber orientation across the inner vessel, wherein the fiber band at least in some of the plies enters from the middle part at a respective entry fiber angle relative to the axis of symmetry into the region of the dome-shaped polar caps.