Microlens has significant applications in integrated micro-optical systems. Recently, multifocal microlens arrays are expected to extend the depth of field for imaging systems and realize a highly efficient laser beam homogenizer. This work presents what we believe to be a novel approach for developing a tunable multifocal liquid crystal microlens array (TMLCMA), which can be operated in convex and concave modes through voltage control schemes. The TMLCMA is manufactured using nematic liquid crystals (LCs) with negative dielectric anisotropy, in conjunction with a triple-electrode structure consisting of top large-hole, middle small-hole array, and bottom planar electrodes. When a voltage is applied, the axially symmetric fringing electric field induced by the large-hole electrode causes the focal length of the microlens to gradually and radially change from the TMLCMA border toward the center. The gradient in the change of focal length is electrically tunable. The calculated spatial potential distributions qualitatively explain the multifocal characteristic and dual lens modes of the TMLCMA. The LC molecules in each microlens are reoriented in an axially symmetrical form, resulting in a polarization-insensitive TMLCMA. The imaging functions of the TMLCMA operated with dual lens modes are shown through practical demonstrations. The simple fabrication and versatile function make the developed TMLCMA highly promising for various optical system applications.