The present study provides a nonlocal beam model for the stress analysis of beams bonded with modulus adhesives using Peridynamic Least Square Minimization (PDLSM) and Refined Zigzag Theory (RZT). RZT is highly useful for the efficient and accurate stress analysis of thin and thick load-bearing structures. RZT avoids the use of shear correction factors to estimate the transverse shear stresses. PDLSM introduces the local derivatives in terms of their nonlocal forms. The PDLSM is applicable for the approximation of any order derivatives. In this study, the PDLSM was employed for the solution of the equilibrium equations of RZT. The robustness of the present approach was demonstrated by considering dissimilar bonded aluminum (Al)-carbon fiber-reinforced polymer composite (CFRP) beam. Modulus graded adhesives have been successfully implemented to minimize the stress concentrations occur in the bonded structures. In order to investigate the effects of the modulus graded adhesive layers on the stress minimization at the critical locations of the bonded beam, various adhesive models were investigated in detail. Each adhesive profile experienced different deformation and stress states. The peak stress levels near the adherend-adhesive interfaces were observed to be alleviated with the use of a modulus graded adhesive layer.