Due to its exceptional mechanical properties, 18CrNiMo7-6 alloy steel is one of the preferred materials for producing critical components of high-speed heavy-duty gearboxes. To study the relationship between cylindrical grinding parameters, i.e., workpiece speed, wheel speed and grinding depth, and grinding responses (grinding force, temperature and surface residual stress), dimensional analysis and finite element simulation of cylindrical grinding for 18CrNiMo7-6 alloy steel are performed. A mathematical model of grinding force and residual stress of cylindrical grinding is proposed, and the numerical and experimental verifications of 18CrNiMo7-6 cylindrical alloy steel are carried out. Numerical verification shows that the maximum relative errors of grinding force and residual stress models are 7.9% and 11.2%, respectively. The experimental results reveal that the maximum absolute errors were 1.31 N and 33.7 MPa, respectively. The results indicate that the proposed model could be used as a guide for practical grinding operation, which is helpful to optimize machining parameters, improve production efficiency and ensure high quality machining results.