The preparation process of terephthalate of dihydric alcohol is one continuous esterification process at the temperature of 258-290 deg.c and pressure 40-120 KPa and in the material molar ratio between dihydric alcohol and terephthalic acid of 1 to 1.5-1.9. The esterification apparatus includes a reactor and an externally circulating shell and tube heater. The reactor has one double-chamber structure including an inner chamber in the bottom of the reactor and an outer chamber. The connecting pipe between the inlet of the heater and the reactor is led to the inner chamber, the connecting pipe between the outlet of the heater and the reactor is led to the outer chamber, and the liquid material passage connecting the inner chamber and the outer chamber is one annular one with U-shaped cross section. The material feeding port is at the inlet of the heater, the liquid reaction product exit is in the bottom of the reactor and led to the inner chamber, and the gas exit is in the top of the reactor. The present invention has lower material ratio between dihydric alcohol and terephthalic acid.