This paper develops an Implicit-Explicit method (IMEX) of third order for solving stiff system of ordinary differential equations (ODEs). The method is $L$-stable with respect to the implicit part and allows the use of an arbitrary approximation of the Jacobian matrix. Order and stability conditions are derived and then solved analytically. Automatic stepsize selection based on local error estimation and stability control is made. The estimations for local error and stability control are obtained without significant additional computational cost. The results of numerical experiments confirm the reliability and efficiency of the implemented integration algorithm.