This paper presents modeling techniques of total-ionization-dose (TID) radiation-induced noise characteristics including dark current (DC), fixed pattern noise (FPN), and equivalent noise charge (ENC) of a CMOS active pixel sensor (APS) for space applications. The noise models from theoretical derivation and experimental data analysis are discussed in detail according to the circuit structure of the CMOS APS based on 4-T transistor pixel topology followed by the column-level correlation double sampling and the column-level amplifier. From the simulation of the theoretical models, the amplitude of noise significantly increases with the increase of total dose, and a threshold dose of ~60 krad (Si) exists. When the total dose is below such threshold, DC, FPN, and ENC increase slowly. When the total dose exceeds the threshold value, these noise parameters increase substantially according to the exponential growth. To verify the proposed models, a $\gamma $ -ray radiation experiment using 60Co source is performed on a commercial 2k $\times \,\, 2\text{k}$ CMOS APS chip in 180-nm CMOS technology from Vendor A. The noise performance of two CMOS APS devices at the dose rates of 50 and 10.6 rad(Si)/s has been measured. It shows that experimental results are in accordance with the rules of theoretical deduction. The dose threshold of the abovementioned three noise parameters is around 60 krad (Si). The TID-induced noise models can be applied to both the design of radiation-hardened CMOS APS and the construction of filtering algorithms in the post image processing.