Conventional acoustic focusing requires an array of actuators or waveguides to form a complex wavefront, resulting in a high cost or bulky size. In this paper, an original gradient Helmholtz-resonator (HR)-based acoustic metasurface (AMS) is presented. The phase shift of AMS units can be precisely controlled over the full phase range and continuously tuned by varying the slit width. The transmission efficiency of the AMSs is relatively high, benefitting from the impedance matching. Several typical situations in acoustic focusing with different focusing parameters are realized by the designed AMSs. The results of the finite element method demonstrate that moving the position of the focal point or changing the incident angle can be realized by tuning the slit width distribution. A further analysis indicates that the discrete resolution is considerably fine, as a result of the suitable deep-subwavelength parameters of the AMS and the high accuracy of the phase shift of each unit. The acoustic intensities at the focal point reach 12.3 to 17.6 times that of the incident plane wave, owing to the high transmission efficiency. Due to these significant advantages, the designed gradient HR-based AMS is able to offer a tuneable acoustic lens in medical sonography, localized heating, nondestructive flaw detection and particle trapping.