Plenoptic cameras have received a wide range of research interest because it can record the 4D plenoptic function or radiance including the radiation power and ray direction. One of its important applications is digital refocusing, which can obtain 2D images focused at different depths. To achieve digital refocusing in a wide range, a large depth of field (DOF) is needed, but there are fundamental optical limitations to this. In this paper, we proposed a plenoptic camera with an extended DOF by integrating a main lens, a tunable multi-focus liquid-crystal microlens array (TMF-LCMLA), and a complementary metal oxide semiconductor (CMOS) sensor together. The TMF-LCMLA was fabricated by traditional photolithography and standard microelectronic techniques, and its optical characteristics including interference patterns, focal lengths, and point spread functions (PSFs) were experimentally analyzed. Experiments demonstrated that the proposed plenoptic camera has a wider range of digital refocusing compared to the plenoptic camera based on a conventional liquid-crystal microlens array (LCMLA) with only one corresponding focal length at a certain voltage, which is equivalent to the extension of DOF. In addition, it also has a 2D/3D switchable function, which is not available with conventional plenoptic cameras.