PURPOSE: To perform cutting work of a compliated shape with improvement of the surface roughness of the cutting surface, by equipping a laser cutting work mechanism and electric discharge machining mechanism controlled by an NC control unit, and providing a process executing means which executes an electric discharge machining on the cutting surface, after the laser cutting.

CONSTITUTION: When a work 14 is fixed to a table mechanism 7 and a composite work device 1 is actuated, the device 1 becomes a laser cutting work mode first. A vertical moving mechanism 8 is then descended along a Z-axis to the position where the focal position of a laser head 10 comes on the surface of the work 14 and cutting is performed by the beam emitted from a laser oscillating device 3 while moving the table mechanism 7 at high speed. A work liquid is then fed to a work tank 11 with the solenoid valve of a work liquid device 5 being opened and the work 14 is placed in the work liquid. The device 1 then comes in a rocking electric discharge machining mode, the end die electrode 15 is arranged in the hole of the work 14 cut off by laser cutting by descending the vertical moving mechanism 8 along Z-axis and the cutting surface of the cutoff hole is finished by diesinking rocking electric discharging.