The ability of any retrieval system to extract features by using its feature descriptor is the primary criterion to measure its efficiency. In this paper a novel technique for feature extraction of biomedical images is presented. The mooted system uses the Radial Associated Laguerre Moments (RALMs) as a feature descriptor to obtain features from two types of medical images: computer tomography (CT) and magnetic resonance images (MRI). RALMs represent one sort of discrete orthogonal moments. RALMs extract the features from images using orthogonal moments to retrieve images from a database. Our approach is extensively assessed with noise-free and noisy images from three different benchmark databases: Emphysema-CT, NEMA CT, and NEMA MRI. The first two databases are used for CT image retrieval, while the third is for MR image retrieval. The proposed approach was tested against the state-of-the art local feature descriptors: Local Binary Pattern (LBP), and local diagonal extrema pattern (LDEP). It was also evaluated against orthogonal Fourier-Mellin moments (OFMMs) as a global descriptor. The comparison shows a significant improvement in favor of the proposed approach in terms of three different performance metrics: ARP, ARR, and F_score. The proposed approach was also compared against the convolutional neural network (CNN) as a deep learning based method over the NEMA-MRI dataset. The RALMs based approach showed a significant improvement when compared against two state-of-the-art medical image retrieval approaches: Histogram of Compressed Scattering Coefficients (HCSCs) and a local bit-plane decodingbased AlexNet descriptor (LBpDAD), the study has done over the TCIA-CT dataset. The proposed approach was also tested with big well-known dataset from the international skin imaging collaboration (ISIC) 2018.