The influence of the off-resonant circularly polarized light on the Josephson current in the time-reversal broken super-conducting Weyl semimetal junctions is investigated by using the Bogoliubov-de Gennes equation and the transfer matrix approach.Both the zero momentum BCS pairing states and the finite momentum Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) pairing states are considered for the Weyl superconductors.When a circularly polarized light is applied,it is shown that the current phase relation remains unchanged for the BCS pairing with the increasing of incident radiation intensity A0.For FFLO pairing,the Josephson current exhibits the 0-π transition and periodic oscillation as a function of A0.The dependence of free energy and critical current on A0 are also investigated.