Abrasive flow machining (AFM) is one of the non-conventional finishing processes used to attain good surface quality and high material removal. However, limited attempts have been made to improve the performance of these processes. This paper presents a novel magnetic abrasive flow machining (MAFM) setup fabricated by adding a magnetization effect in which a nylon fixture and permanent magnets are replaced by a newly fabricated aluminium fixture and coil-type magnets, respectively. Inner cylindrical surfaces of hybrid Al/SiC/B4C metal matrix composites (MMCs) are finished by the MAFM process. One variable at a time (OVAT) approach is used for studying the effect of 6 input parameters, extrusion pressure (Ep), the number of cycles (N), abrasives concentration (C), workpiece material (Wp), abrasive mesh size (M), and magnetic flux density (Mf) upon response parameters, material removal rate (MRR) and change in surface roughness (ΔRa). The experimental results obtained for MRR and ΔRa show a significant improvement from 3.92 to 7.68 μg/s and 0.49 to 0.74 μm, respectively due to the increase of the extrusion pressure from 1 to 9 Mpa. The MRR and ΔRa was reduced from 6.89 to 6.78 μg/s and 0.46 to 0.22 μm, respectively with an increase in mesh number of abrasives from 80 to 400. The variation in concentration of abrasives from 40 to 60 % shows an improvement in MRR from 4.51 to 6.42 μg/s; whereas, there is a negligible effect on ΔRa which comes out from 3.82 to 3.86 μm. The MMCs, which are used for the experimentation shows a decline in MRR and ΔRa from 5.12 to 3.85 μg/s and 0.77 to 0.42 μm, respectively. This happened because there was a percentage change of reinforcement of SiC from 9 to 7 % and B4C from 1 to 3 % in Al-6063. An increase in the number of cycles from 50 to 250 shows a significant improvement in both MRR and ΔRa from 1.79 to 3.75 μg/s and 0.97 to 1.86 μm, respectively. Variation in magnetic effect also significantly improves MRR and ΔRa from 1.35 to 3.17 μg/s and 0.38 to 1.06 μm, respectively, when it is varied from 0.15 - 0.45 Tesla. The work carried out shows an overall significant improvement in MRR and ΔRa by using the MAFM process. The MAFM process finds a wide range of applications in finishing like surgical instruments, mechanical components, aerospace industry, electronics industry, etc. HIGHLIGHTS The hybrid MMCs (Al/SiC/B4C) are finished by novel MAFM setup An aluminium fixture and coil-type magnets play a significant role for finishing the workpiece surfaces An abrasive laden media acts as a cutting tool in the finishing process The OVAT approach is used for investigating the parametric effect The extrusion pressure, number of cycles and magnetic flux density are the significant parameters affecting the MRR and ΔRa GRAPHICAL ABSTRACT