To provide a power transmission shaft coupling, for smoothly transmitting torque free of irregularities in rotation or vibrations, by completely absorbing misalignment between a drive side shaft and a driven side shaft and play in a rotation direction even in shafting intersecting the drive side shaft with the driven shaft with a certain angle.

A cylindrical coupling is interposed between a drive gear and a driven shaft, and a circular fitting part of the drive gear is fitted in an inner circumference of the coupling so that relative rotation is regulated and relative movement in an axial direction is allowed. A second coupling is installed to a shaft end part of the driven shaft not to be relatively rotated, and the second coupling is connected with the other end side of the coupling to be disengageable by meshing of engagement teeth formed along a circumferential direction at two parts with engagement grooves.