This paper focuses on a class of delayed fractional Cohen–Grossberg neural networks with the fractional order between 1 and 2. Two kinds of criteria are developed to guarantee the finite-time stability of networks based on some analytical techniques. This method is different from those in some earlier works. Moreover, the obtained criteria are expressed as some algebraic inequalities independent of the Mittag–Leffler functions, and thus, the calculation is relatively simple in both theoretical analysis and practical applications. Finally, the feasibility and validity of obtained results are supported by the analysis of numerical simulations.