Each curve belongs to a multivariate nonparametric regression model, and many shape-invariant curves form a curve family connected with a reference curve by some parameters. Curve drift models can be built to forecast many curves in practice. In this paper, we put forward the multivariate nonparametric regression mental curve drift model after our study of the mental curves of visual scenes composing. However, the multivariate nonparametric regression mental curve drift model is very complicated to trace. And we apply neural networks to solve this problem. Neural networks have been shown to be particularly effective in handling some complexities commonly found in complicated regression models and datum. Here, we apply neural networks to fit the curves family and to forecast the mental curves with curve drift. An example is provided to show the feasibility of curve drift and mental curve tracing with neural networks.