We propose a high thermal conductivity infrared (IR) filter using alumina for use in millimeter wave detection systems. We constructed a prototype two-layer anti-reflection (AR) coated alumina filter with a diameter of 100 mm and a thickness of 2 mm, and characterized its thermal and optical properties. The transmittance of this filter at 95 GHz and 150 GHz is 97 % and 95 % while the estimated 3 dB cutoff frequency is at 450 GHz. The high thermal conductivity of alumina minimizes thermal gradients. We measure a differential temperature of only 0.21 K between the center and the edge of the filter when it is mounted on a thermal anchor of 77 K. We also constructed a thermal model based on the prototype filter and analyzed the scalability of the filter diameter. We conclude that temperature increase at the center of alumina IR filter is less than 6 K even with a large diameter of 500 mm, when the temperature at the edge of the filter is 50 K. This is suitable for an application to a large-throughput next-generation cosmic microwave background (CMB) polarization experiment, such as POLARBEAR-2 (PB-2).