This paper focuses on the finite-time synchronization analysis for complex-valued recurrent neural networks with time delays. First, two kinds of common activation functions appearing in the existing references are combined together and more general assumptions are given. To achieve our aim, a nonlinear delayed controller with two independent parameters different from the existing ones is provided, which leads to great difficulty. To overcome it, a newly developed inequality is used. Then, via Lyapunov function approach, some criteria are derived to guarantee (...) the finite-time synchronization of the considered system, and the settling time for synchronization is also estimated. Finally, two numerical simulations are given to support the effectiveness and advantages of the obtained results. (shrink)