Stellar perturbations affect planet formation in binary systems. Recent studies show that the planet-formation stage of mutual accretion of km-sized planetesimals is most sensitive to binary effects. In this paper, the condition for planetesimal accretion is investigated around α CenB, which is believed to be an ideal candidate for detection of an Earth-like planet in or near its habitable zone (0.5-0.9 AU). A simplified scaling method is developed to estimate the accretion timescale of the planetesimals embedded in a protoplanetary disk. Twenty-four cases with different binary inclinations (i_B = 0, 01, 10, and 10°), gas densities (0.3, 1, and 3 times of the Minimum Mass of Solar Nebula, MMSN hereafter), and with and without gas depletion, are simulated. We find that (1) re-phasing of planetesimals orbits is independent of gas depletion in α CenB, and it is significantly reached at 1-2 AU, leading to accretion-favorable conditions after the first ~ 10⁵ yr; (2) the planetesimal collision timescale at 1-2 AU is estimated as: T^B _col ~ (1 + 100i_B ) × 10³ yr, where 0° < i_B < 10°; (3) disks with gas densities of 0.3-1.0 MMSN and inclinations of 1°-10° with respect to the binary orbit are found to be the favorable conditions in which planetesimals are likely to survive and grow up to planetary embryos; and (4) even for the accretion-favorable conditions, accretion is significantly less efficient as compared to the single-star case, and the time taken by accretion of km-sized planetesimals into planetary embryos or cores would be at least several times of T^B _col, which is probably longer than the timescale of gas depletion in such a close binary system. In other words, our results suggest that formation of Earth-like planets through accretion of km-sized planetesimals is possible in α CenB, while formation of gaseous giant planets is not favorable.