The present invention discloses an analog to digital conversion (ADC) apparatus having quick conversion mechanism. Each of ADC circuits receives a previous higher-bit conversion result to perform prediction to generate a current higher-bit conversion result, performs conversion on an input analog signal according to a sampling clock that has a frequency at least twice of the frequency of the input analog signal based on a successive-approximation mechanism to generate a current lower-bit conversion result, and combines the current higher-bits and current lower-bit conversion results to generate a current conversion result and output a remained signal amount as a residue. A noise-shaping circuit performs calculation based on the residue to generate a noise-shaping reference signal. Each of the ADC circuits combines the current conversion result and the noise-shaping reference signal to generate an output digital signal.