The GaN high electron mobility transistor (HEMT) has been considered as a potential terahertz (THz) radiation source, yet the low radiation power level restricts their applications. The HEMT array is thought to improve the coupling efficiency between two-dimensional (2D) plasmons and THz radiation. In this work, we investigate the plasma oscillation, electromagnetic radiation, and the integration characteristics of GaN HEMT targeting at a high THz radiation power source. The quantitative radiation power and directivity are obtained for integrated GaN HEMT array with different array periods and element numbers. With the same initial plasma oscillation phase among the HEMT units, the radiation power of the two-element HEMT array can achieve 4 times as the single HEMT radiation power when the array period is shorter than 1/8 electromagnetic wavelength. In addition, the radiation power of the HEMT array varies almost linearly with the element number, the smaller array period can lead to the greater radiation power. It shows that increasing the array period could narrow the main radiated lobe width while weaken the radiation power. Increasing the element number can improve both the radiation directivity and power. We also synchronize the plasma wave phases in the HEMT array by adopting an external Gaussian plane wave with central frequency the same as the plasmon resonant frequency, which solves the problem of the radiation power reduction caused by the asynchronous plasma oscillation phases among the elements. The study of the radiation power amplification of the one-dimensional (1D) GaN HEMT array provides useful guidance for the research of compact high-power solid-state terahertz sources.