Recent observations show that planets can reside in close binary systems with stellar separation of only ~20 AU. However, planet formation in such close binary systems is a challenge to current theory. One of the major theoretical problems occurs in the intermediate stage—planetesimals accretion into planetary embryos—during which the companion's perturbations can stir up the relative velocities (V) of planetesimals and thus slow down or even cease their growth. Recent studies have shown that conditions could be even worse for accretion if the gas-disk evolution was included. However, all previous studies assumed a two-dimensional disk and a coplanar binary orbit. Extending previous studies by including a three-dimensional gas disk and an inclined binary orbit with small relative inclination of i_B = 01-5°, we numerically investigate the conditions for planetesimal accretion at 1-2 AU, an extension of the habitable zone (~1-1.3 AU), around α Centauri A in this paper. Inclusion of the binary inclination leads to the following: (1) differential orbital phasing is realized in the three-dimensional space, and thus different-sized bodies are separated from each other, (2) total impact rate is lower, and impacts mainly occur between similar-sized bodies, (3) accretion is more favored, but the balance between accretion and erosion remains uncertain, and the "possible accretion region" extends up to 2 AU when assuming an optimistic Q* (critical specific energy that leads to catastrophic fragmentation), and (4) impact velocities (V) are significantly reduced but still much larger than their escape velocities, which infers that planetesimals grow by means of type II runaway mode. As a conclusion, the inclusion of a small binary inclination is a promising mechanism that favors accretion, opening a possibility that planet formation in close binary systems can go through the difficult stage of planetesimals accretion into planetary embryos.