Zeroing neural network (ZNN) with different activation functions (AFs) for finding zero-result of time-varying quadratic programming (TVQP) with no noises are revisited. To improve the convergent speed of the ZNN and resist various noises occurred in the real application, two robust terminal recurrent neural network (RTRNN) models by adding two different AFs are presented for the exact solution of the TVQP problem facing various noises. The appearing advantage of the prespecified time of the RTRNN model is independent of the initial status of a generated system and the convergent time can be accelerated in advance, which is much superior than the finite-time performance with regard to the initial status. In addition, the prespecified convergent time of the RTRNN is mathematically discussed in detail under external noises. Simulated comparisons between the proposed RTRNN and the state-of-the-art neural networks substantiate the predefined time performance and strong robustness.