This paper presents a type of wide band micro-perforated panel (MPP) absorber with an array of parallel arranged sub-cavities at different depths based on the quadratic residue sequence (QRS). An analytical prediction model is proposed for evaluating the normal incidence sound absorption coefficients of this type of MPP absorber in its design stage. Next, simulations with a finite element procedure and experimental measurements were conducted to provide cross-validations of the proposed analytical model and to facilitate the discussions on the sound absorption performance of this type of MPP absorber. The results show that the analytical model provides simple yet accurate prediction on the sound absorption performance of this MPP absorber; the absorption bandwidth of this type of MPP absorber can be significantly enhanced through the fine design on the sub-cavity depth sequence. It is also shown that the normal incidence absorption coefficient of this type of MPP absorber can remain beyond 0.5 in the frequency range of 450–3500 Hz, with the maximum value of 0.98.