We are developing a superconducting Transition-Edge Sensor (TES) calorimeter array. We adopt calorimeter multiplex in frequency domain to read signals from the calorimeter array with a small number of front-end electronics and wirings. We further utilize Calorimeter Bridge Biased by an AC Generator (CABBAGE) approach to eliminate the AC carrier in the output. We tested the method using a TES calorimeter, which has a transition temperature of 390 mK. Because of the high operating temperature, energy resolution of the calorimeter is limited to 200 eV at 5.9 keV even when it is biased with a DC current. We operated the calorimeter in CABBAGE circuit with 30 kHz sinusoidal bias and obtained an energy resolution of 250 eV. We found that there remains a small-amplitude residual in the output even at the bridge balance point. The residual contains not only 30 kHz component but also odd-order harmonics. We consider that this is due to the variation of the TES resistance with bias current. The 50 eV degradation of the energy resolution from DC to AC biases can be explained by the fact that some of signal power is carried in the odd-order harmonics, which we did not utilize in the data reduction process. We also succeeded to operate the CABBAGE by 100 kHz, although the energy resolution was degraded to 380 eV probably due to low response of the signal readout circuit at the frequency.