We theoretically investigate the high-order harmonic generation from a neon atom irradiated by an intense two-color femtosecond laser pulse, in which the fundamental field and its second harmonic are linearly polarized and orthogonal to each other. In contrast to usual high-harmonic generation with linearly polarized fundamental field alone, a very strong and clean high-harmonic spectrum, consisting of both odd and even orders of harmonics, can be generated in the orthogonally polarized two-color laser field with proper selection of the relative phase between the fundamental and second-harmonic fields. In time domain, this results in a strong and regular attosecond pulse train. The origin of these behaviors is elucidated by analyzing semiclassical electron paths and by simulating high-harmonic generation quantum mechanically.