We propose an off-axis relativistic jet model for the Type Ic supernova SN 2007gr . Most of the energy ( \sim 2 \times 10 ^ { 51 } erg ) in the explosion is contained in non-relativistic ejecta which produces the supernova . The optical emission is coming from the decay process of ^ { 56 } Ni synthesized in the bulk SN ejecta . Only very little energy ( \sim 10 ^ { 48 } erg ) is contained in the relativistic jet with initial velocity about 0.94 times the speed of light . The radio and X-ray emission comes from this relativistic jet . With some typical parameters of a Wolf-Rayet star ( progenitor of Type Ic SN ) , i.e. , the mass loss rate \dot { M } = 1.0 \times 10 ^ { -5 } ~ { } M _ { \odot } ~ { } yr ^ { -1 } and the wind velocity v _ { w } = 1.5 \times 10 ^ { 3 } ~ { } km~ { } s ^ { -1 } together with an observing angle of \theta _ { obs } = 63.3 ^ { \circ } , we can obtain the multiband light curves that fit the observations well . All the observed data are consistent with our model . Thus we conclude that SN 2007gr contains a weak relativistic jet and we are observing the jet from off-axis .