In modern applications such as robotics, autonomous vehicles, and speaker localization, the computational power for sound source localization applications can be limited when other functionalities get more complex. In such application fields, there is a need to maintain high localization accuracy for several sound sources while reducing computational complexity. The array manifold interpolation (AMI) method applied with the Multiple Signal Classification (MUSIC) algorithm enables sound source localization of multiple sources with high accuracy. However, the computational complexity has so far been relatively high. This paper presents a modified AMI for uniform circular array (UCA) that offers reduced computational complexity compared to the original AMI. The complexity reduction is based on the proposed UCA-specific focusing matrix which eliminates the calculation of the Bessel function. The simulation comparison is done with the existing methods of iMUSIC, the Weighted Squared Test of Orthogonality of Projected Subspaces (WS-TOPS), and the original AMI. The experiment result under different scenarios shows that the proposed algorithm outperforms the original AMI method in terms of estimation accuracy and up to a 30% reduction in computation time. An advantage offered by this proposed method is the ability to implement wideband array processing on low-end microprocessors.