To miniaturize the double-resonance (DR) rubidium (Rb) vapor-cell atomic clocks, a new type of micro-loop-gap microwave resonator (mu-LGR) is proposed for TE011-like mode where the magnetic field inside the cavity is homogeneous and oriented along its longitudinal axis over a large volume. It provides more design degrees of freedom by elaborating the printed pattern in the middle layer, while the mechanical strength of the cavity is strong. It also possesses a wider tuning range of the resonances in order to compensate the fabrication tolerances on such miniature precision devices. A theoretical analysis of the general mu-LGR without tuning is presented first, serving as the basic guideline to design the tunable mu-LGR. To demonstrate the wide tuning mechanism, an equivalent circuit model and different tuning schemes are discussed. The measured results show that the proposed tunable mu-LGR can operate at 6.835 GHz by properly adjusting the tuning screw position. Compared to the existing mu-LGRs, this new design can achieve a 40% volume reduction (572 mm(3), approaching the physical limit) and a comparable magnetic field quality, and enlarges the frequency tuning range to 260 MHz (twofold) in measurement. Thus, the proposed compact tunable mu-LGR has a high potential in miniature vapor-cell atomic frequency standards.