Recently, two-dimensional (2D) multiferroic materials have aroused intensive interest owing to the combination of ferroelectric and magnetic properties. In this work, we design a family of 2D MSX₂ (M = Zr and Nb; X = Cl, Br, and I) and investigated their structural, mechanical, magnetic, electronic, ferroelectric, and piezoelectric properties based on first-principles calculations. We find that ferroelectric (FE) ZrSX₂, paraelectric (PE) ZrSX₂ and FE NbSX₂ are stable. ZrSX materials are nonmagnetic, while NbSX materials have antiferromagnetic (AFM) ground states. NbSX materials demonstrate multiferroic behaviors, which can be explained by the pseudo Jahn-Teller distortion (PJTE) mechanism. Our work reveals the intrinsic multiferroicity of MSX₂, which may provide a guidance on the design of 2D functional materials.