We study theoretically and numerically the manipulation of Raman-induced frequency shift (RIFS) with chirped Airy pulse in the optical fiber. The results show that the blue-shift of Airy pulse increases with the increase of the positive chirp parameter and so the RIFS can be suppressed. The red-shift of Airy pulse increases with the increase of the truncation coefficient and so the RIFS can be enhanced. In addition, the effect of the initial pulse width on the RIFS is discussed. The results show that the larger the launched pulse width, the stronger the RIFS of the pulse. And it is more obvious to suppress the RIFS with the increase of the positive chirp. Therefore, the RIFS of Airy pulse can be controlled effectively by adjusting the chirp or the truncation coefficient with different initial pulse width.