This work develops a third-order multibit switched-current (SI) delta-sigma modulator (DSM) with a four-bit switched-capacitor (SC) flash analog-to-digital converter (ADC) and an incremental data weighted averaging circuit (IDWA), which is fabricated using 0.18µm 1P6M CMOS technology. In the proposed DSM, a 4-bit SC flash ADC is used to improve its resolution, and an IDWA is used to reduce the nonlinearity of digital-to-analog converter (DAC) by moving the quantization noise out of the signal band by first-order noise shaping. Additionally, the proposed differential sample-and-hold circuit (SH) exhibits low input impedance with feedback and width-length adjustment in the SI feedback memory cell (FMC) to increase the conversion rate. A coupled differential replicate (CDR) common-mode feedforward circuit (CMFF) is used to compensate for the mirror error that is caused by the current mirror. Measurements indicate that the signal-to-noise ratio (SNR), dynamic range (DR), effective number of bits (ENOB), power consumption, and chip area are 64.1 dB, 64.4 dB, 10.36 bits, 18.82 mW, and 0.45 × 0.67 mm2 (without I/O pad), respectively, with a bandwidth of 20 kHz, an oversampling ratio (OSR) of 256, a sampling frequency of 10.24 MHz, and a supply voltage of 1.8 V.