In recent years,accelerating waves have attracted great research interests both due to their unique properties and tempting applications.Here we investigate the effect of the inter-particle interaction on accelerating of Bose-Einstein condensate (BEC).We show that spatially homogeneous interactions will have no accelerating effect on BEC regardless of the interaction form (contact,dipole-dipole,or any others).But spatially inhomogeneous interactions may lead to an accelerating motion of the condensate.As an example,the accelerating dynamic of BEC under a spatially linear modulated contact interaction is studied in detail.It is found that such an interaction will accelerate the condensate with a time varying acceleration.Furthermore,an interaction engineering scheme to achieve constantly accelerating BEC is proposed and studied numerically.Numerical results suggest that this engineering scheme can also suppress profile changing of the condensate during its evolution,thus realize an accelerating profile-keeping matter wave packet.Our analysis also applies to optical waves with Kerr nonlinearity.