The stability, atomic structural and magnetic properties of ultrathin Cr films on W(100) and W(110) substrates are studied by using ab-initio total energy calculations. It is demonstrated that the overlayer structures of monolayer (ML) Cr on W(100) or W(110) substrates are stable against the interdiffusion. Large top-layer downward relaxations are found for both the systems. The relationship between relaxation and magnetic configuration is also analysed. The magnetic ground state is found to be p(1 × 1) ferromagnetic and c(2 × 2) antiferromagnetic with enhanced magnetic moments of 2.47 μB and 2.55 μB for 1 ML Cr on W(100) and W(110) substrates, respectively.