Multi-term variable-order fractional differential equations (VO-FDEs) are considered to be one of the tools to illustrate the behavior of transient-regime real-life phenomena precisely. The analytical solutions of VO-FDEs are generally very hard to obtain. Therefore, in this study, an approximation method for the solution of multi-term VO-FDEs is proposed using shifted Chebyshev polynomials of the third kind (SCP3). The method employs the operational matrices of SCP3 to proximate the VO-FDEs with a system of algebraic equations. The solution of which also yields the approximate result for the multi-term VO-FDE. An error analysis is also included. The SCP3 method is examined on several examples demonstrating the precision and prowess of the method. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).