Canonical correlation analysis (CCA) is a multivariate linear model that has been used for seasonal prediction of climate fields. Recently, nonlinear versions of CCA have been proposed, including several that rely on neural network architectures. For example, nonlinear CCA (NLCCA) models based on the multilayer perceptron neural network can be used to identify linked nonlinear modes of variability between two multivariate datasets. For datasets with low signal-to-noise ratios, parameter estimates in the NLCCA model can be unstable and models can overfit easily. While these problems can be mitigated through the use of regularization terms in the cost functions and ensemble averaging methods, real-world performance can still lag behind the linear CCA model. As an alternative, a robust version of NLCCA (R-NLCCA) is introduced that replaces the non-robust cost functions in the model (i.e., the Pearson product moment correlation and the mean squared error) with robust alternatives (i.e., the biweight midcorrelation and mean absolute error). R-NLCCA is applied to seasonal prediction of sea surface temperature anomalies(SSTA) in the tropical Pacific Ocean at lead times from 0-12 months. Cross-validation analysis suggests that R-NLCCA models can be estimated more robustly than NLCCA models. R-NLCCA models are also more skillful than NLCCA models, particularly at longer lead times.