Precise control of the laser focal position in the relativistic laser–plasma interaction is crucial for electron acceleration, inertial confinement fusion, high-order harmonic generation, etc. However, conventional methods are characterized by limited tunability and rapid divergence of the relativistic laser pulse after passing through a single focal point. In this work, we propose a novel plasma lens with a density gradient to achieve laser focusing in a tunable focal volume. The capacity depends on the modification of the phase velocity of the incident seed laser propagating in plasma. By modifying the plasma density gradient, one can even achieve an off-axis focusing plasma lens, allowing the laser to be focused further at an adjustable focus. Based on this new type of optical device, a beam-splitting array is also proposed to leverage this unique focusing mechanism for the generation of strong axial magnetic fields (>1000 T). Three-dimensional particle-in-cell simulations demonstrate that the seed laser with a focal spot of $9\ \unicode{x3bc} \mathrm{m}$ passing through the density varying plasma lens exhibits a focused laser with a focal spot of approximately $2.3\ \unicode{x3bc} \mathrm{m}$ and an 18 times enhancement of the laser intensity. The approach has considerable potential for applications in several areas, including laser-driven particle acceleration, X/$\gamma$-ray emission, strong magnetic field generation, etc.