In view of the great importance of dynamical behavior prediction of nanostructures in contact with fluid and their vast range of applications in biomedical engineering, aerospace, etc., in this research, the free vibration of a Nanoscale Euler-Bernoulli rotating beam coupled with incompressible viscous fluid is studied. Small-scale effects are applied by using nonlocal elasticity theory. Using the Navier-Stokes relation, the interaction forces between the fluid and nanobeam are obtained. Governing differential equations have been solved by Galerkin method and the system vibrations frequency response has been obtained for clamped-free boundary condition. Based on the results of this research, nonlocal elasticity has a different effect on different vibration modes. The frequency of the nanobeam coupled with the fluid quickly increases when applying this theory, and the presence of fluid reduces the natural frequencies.