Discovering new two-dimensional (2D) Dirac semimetals incorporating both superconductivity and the topological band structure provides a novel platform for realizing the intriguing applications of massless Dirac fermions and Majorana quasiparticles, ranging from high-speed quantum devices at the nanoscale to topological quantum computations. In this work, utilizing first-principles calculations and symmetry analysis, we introduce MOH (M= Zr, Hf) as a new topological Dirac superconductor with Dirac points close to a Fermi level which are connected with nearly flat edge states as a striking feature of topological semimetals. Our calculations show that ZrOH as a 2D Dirac semimetal can exhibit superconductivity and is a novel platform for studying the interplay between superconductivity and Dirac states in low-dimensional materials.