In this study, an iterative learning control (ILC) algorithm is proposed to improve synchronous errors in rigid tapping. In rigid tapping, the displacements of the z‐axis and spindle must be kept synchronous to prevent damage. Using learning control provides better commands for both the z‐axis and spindle dynamics, improving the synchronicity of the output responses of the z‐axis and spindle. The proposed ILC makes use of synchronous errors in the previous cycle of tapping to modify the current position commands of both the z‐axis and spindle. A systematic algorithm is proposed for the computation of learning gains that guarantee the monotonic convergence of synchronous errors. A systematic procedure of applying ILC to rigid tapping is also proposed, where the ideas of effective learning gains and stop learning criteria are discussed. Experimental results on a tapping machine verify the effectiveness of the proposed ILC algorithm.