  The (1+1)-dimensional kinetic model of crystal growth with simulated
self-attraction and random sequential or parallel dynamics is introduced and
studied via Monte-Carlo simulations. To imitate the attraction of absorbing
atoms the probability of deposition is chosen to depend on the number of the
nearest-neighbor atoms surrounding the deposited atom so it increases with this
number. As well the evaporation probabilities are chosed to roughly account for
this self-attraction. The model exhibits the interface depinning transition
with KPZ-type roughness behavior in the moving phase. The critical indices of
the correlation lengths are $\nu_\parallel = 0.82 \pm 0.03,{\rm{}}\nu_ \bot =
0.55 \pm 0.02$ and the critical index of the growth velocity is $1.08 \pm 0.03$
indicating the new universality class of the depinning transition. The critical
properties of the model do not depend on the type of dynamics implemented.
