The problem associated with the stiff ordinary differential equation (ODE) systems in parallel processing is that the calculus can not be started simultaneously on many processors with an explicit formula. The proposed algorithm is constructed for a special classes of stiff ODE, those of the form y′(t)=A(t)y(t)+g(t). It has a high efficiency in the implementation on a distributed memory multiprocessor when the ODEs function has many components. The approximation error is equal to that produced by the analogous sequential algorithm.