In the millimeter-wave bands, the series-fed array antenna is facing a problem of large transmission loss and narrow bandwidth by using a high permittivity and large-loss tangent material. In this report, an air-layer is inserted in a LTCC waveguide of dielectric constant=6.6 and loss tangent=0.013 to reduce the transmission loss. The reduction of the equivalent dielectric constant by the air insertion structure enhances both the gain and the bandwidth of the series-fed slot array. We confirm these by measuring the single-mode waveguides and the one-dimensional series-fed slot arrays. The transmission loss of the single-mode rectangular waveguide has been reduced to 1/6 by using the partially-filled structure. The total gain has been enhanced by 8dB. The 3dB bandwidth has also been increased from 1.3GHz to 2.3GHz enhanced in the 60GHz band.