The current study analyzes the nonlinear free vibration of Euler–Bernoulli microbeams manufactured from bi-directional functionally-graded (BFG) material with geometric imperfection. In order to explore the small-scale impacts on free vibration, the modified couple stress theory is utilized. Moreover, the Hamilton principle is used for determining the underlying partial differential equations along with the boundary conditions. Afterwards, the underlying equations are solved using the differential quadrature method (DQM) as well as the direct iterative method. The proposed model is verified through comparing the obtained results with benchmark results obtained from previous studies. Furthermore, a number of numerical examples are presented as a means to explore the impacts of material length scale parameter, geometric imperfection parameter, material property gradient index and end support on the nonlinear frequency of the BFG microbeams. As a main result, it is observed that the nonlinear vibration frequencies are greater than the linear vibration frequencies.