The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. Motivated by some explicit examples of singular integral operators studied in Ricci and Stein (Ann Inst Fourier (Grenoble) 42:637–670, 1992), Fefferman and Pipher (Am J Math 11:337–369, 1997), and Nagel and Wainger (Am J Math 99:761–785, 1977), we introduce a class of singular integral operators on $${\mathbb {R}}^3$$ R 3 associated with Zygmund dilations by providing suitable version of regularity conditions and cancellation conditions on convolution kernels, and then show the boundedness for this class of operators on $$L^p$$ L p , $$1<p<\infty $$ 1 < p < ∞ .