Free controls of optic/acoustic waves for bending, focusing or steering the energy of wavefronts are highly desirable in many practical scenarios. However, the dispersive nature of the existing metamaterials/metasurfaces for wavefront manipulation necessarily results in limited bandwidth. Here, we propose the concept of dispersionless wavefront manipulation and report a theoretical, numerical and experimental work on the design of a reflective surface capable of controlling the acoustic wavefront arbitrarily without bandwidth limitation. Analytical analysis predicts the possibility to completely eliminate the frequency dependence with a specific gradient surface which can be implemented by designing a subwavelength corrugated surface. Experimental and numerical results, well consistent with the theoretical predictions, have validated the proposed scheme by demonstrating a distinct phenomenon of extraordinary acoustic reflection within an ultra-broad band. For acquiring a deeper insight into the underlying physics, a simple physical model is developed which helps to interpret this extraordinary phenomenon and predict the upper cutoff frequency precisely. Generations of planar focusing and non-diffractive beam have also been exemplified. With the dispersionless wave-steering capability and deep discrete resolution, our designed structure may open new avenue to fully steer classical waves and offer design possibilities for broadband optical/acoustical devices.