  We introduce branching annihilating attracting walk (BAAW) in one dimension.
The attracting walk is implemented by a biased hopping in such a way that a
particle prefers hopping to a nearest neighbor located on the side where the
nearest particle is found within the range of attraction. We study the BAAW
with four offspring by extensive Monte Carlo simulation. At first, we find the
critical exponents of the BAAW with infinite range of attraction, which are
different from those of the directed Ising (DI) universality class. Our results
are consistent with the recent observation [B. Daga and P. Ray, Phys. Rev. E
{\bf 99}, 032104 (2019)]. Then, by studying crossover behaviors, we show that
as far as the range of attraction is finite the BAAW belongs to the DI class.
We conclude that the origin of non-DI critical behavior of the BAAW with
infinite range of attraction is the long-range nature of the attraction.
