The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are imprints of the spacetime events representing emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources.