Microbeams are one of the most important members of microelectromechanical systems (MEMS) which contrast of electrical and mechanical forces in them cause pull-in instability. One of the proposed mechanisms for controlling this instability and enlarging the stable range of system are initially curved microbeams. Despite studying various pull-in instability in straight elastic or viscoelastic microbeams, the instability of curved microbeams has been investigated only within the range of elastic behavior. Therefore in the present study, assuming a clamped-clamped viscoelastic initially curved microbeam, the effect of viscoelastic behavior on the instabilities called snap-through and pull-in, was investigated. The viscoelastic behavior was simulated by the standard anelastic linear solid model. The governing differential equation was obtained based on the modified couple stress theory and by use of Hamilton’s pull-in instability principle. By using the Galerkin method, the governing equation was converted to a nonlinear ordinary differential equation and solved by MATLAB sofware. The structure behaviors are compared in two extreme situations before and after the viscoelastic relaxation by drawing diagrams. The results show when the time of structure relaxation increases, viscoelastic behavior causes more decreasing in instabilities voltage, but its effect on the position of instability will depend on the axial load. In this way, in the presence of tensile load, viscoelastic behavior increases the snap-through position and decreases the pull-in position, but in the presence of compressive load, snap-through occurs at smaller deflections and pull-in occurs at larger deflections.