By taking the vectorial property of the time-average enregy flow density into account, a new extensive definition of the light intensity is proposed. It is expressed as the time average of the amount of energy which crosses in a unit time and a unit area, so it can be applied to any point at any curved surface. This definition is directly related to the measurement quantity of the light intensity on a curved surface. The intensity formula shows that the light intensity at any point of a curved surface is not only related to the amplitude at the point, but also related to the included angle between the Poynting vector (time average) and the direction of the local differential surface element. Especially, as an important consequence, the light intensity on the transverse plane perpendicular to the propagation axis is given. These results can be used to study the second intensity moments and the M2 factor of the non-paraxial beams.