Vortex beams accompanied with orbital angular momentum have attracted significant attention in research fields due to their formidable capabilities in various crucial applications. However, conventional devices for generating vortex beams still suffer from bulky sizes, high cost, and confined performances. Metalens, as an advanced platform to arbitrarily control the optical waves, has promising prospects to address the predicament for conventional devices. Although great progress has been demonstrated in the applications of vortex beams, they are still confronted with fixed functionality after fabrication that severely hinders their application range. In this work, the phase-change material of Ge2Sb2Te5 (GST) is employed to design the meta-atoms to realize tunable optical responses. Moreover, the focused vortex beam can be accomplished by superimposing a helical phase and hyperbolic phase, and the chromatic aberrations in near-infrared (NIR) range can be corrected by introducing an additional phase compensation. And the design strategy is validated by two different metalenses (BAMTF-1 and BAMTF-2). The numerical results indicate that the chromatic aberrations for two metalens can be corrected in 1.33-1.60 mu m covering the telecom range. Moreover, the average focusing efficiency of BAMTF-1 is 51.4%, and that of BAMTF-2 is 39.9%, indicating the favorable performances of designed BAMTF. More importantly, their average focal lengths have a relative tuning range of 38.82% and 33.17% by altering the crystallization ratio of GST, respectively. This work may provide a significant scheme for on-chip and tunable devices for NIR imaging and communication systems.