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 alpha 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, 0 degrees.1, 1 degrees.0, and 10 degrees), 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 alpha CenB, and it is significantly reached at 1-2 AU, leading to accretion-favorable conditions after the first similar to 10(5) yr; (2) the planetesimal collision timescale at 1-2 AU is estimated as: T(col)(B) similar to (1 + 100i(B)) x 10(3) yr, where 0 degrees < i(B) < 10 degrees; (3) disks with gas densities of 0.3-1.0 MMSN and inclinations of 1 degrees-10 degrees 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(col)(B), 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 alpha CenB, while formation of gaseous giant planets is not favorable.