A 3D-printed all-dielectric metasurface is presented in this Letter which can generate an accelerating beam with a circularly symmetric non-spreading transverse profile that can propagate along arbitrary convex trajectories. The curved trajectory is mapped to the corresponding direct-space spatial phases by the basic cube units with different geometrical heights. The required phase distribution is derived in detail based on the enveloping theory of differential geometry and the Bessel beam generation method. A metasurface with a preset trajectory is simulated and measured to demonstrate the validity of the phase distribution calculated by the proposed theory. The full-wave simulation and measurement results verify that the Bessel-like beam whose intensity follows a curved (off-axis) trajectory can be produced by the proposed metasurface. The generated hybrid beam merges the advantages of non-accelerating and accelerating diffractive-free beams. Therefore, the proposed metasurface has great potential in ultrahigh-speed communication, secure communication, near-field imaging, wireless energy transmission applications, and so on. The all-dielectric characteristic provides the proposed metasurface with the competitive advantages of low cost and easy large-scale processing.