A model of turbulent premixed flame initiation and early stage of propagation is proposed. Initiation submodel consists in representing of spark action with the heat deposit of the energy and duration appropriate for conditions relevant to SI engine, that is with the spark duration being non-negligible compared with turbulent time-scale. Chemistry is represented with reduced kinetics scheme of six reactions coupled with the pdf approach. The results of simulations obtained with this model are discussed. In particular, they show the model proposed is able to yield reasonable values for low concentration limits of ignition as well as critical spark energy needed to obtain self-sustaining flame propagation.