Data-driven process monitoring has benefited from the development and application of kernel transformations, especially when various types of nonlinearity exist in the data. However, when dealing with the multimodality behavior which is frequently observed in process operations, the most widely used Radial Basis Function kernel has limitations in describing process data collected from multiple normal operating modes. In this paper, we highlight this limitation via a synthesized example. In order to account for the multimodality behavior and improve fault detection performance accordingly, we propose a novel Non-stationary Discrete Convolution kernel, which derives from the convolution kernel structure, as an alternative to the RBF kernel. By assuming the training samples to be the support of the discrete convolution, this new kernel can properly address these training samples from different operating modes with diverse properties, and therefore can improve the data description and fault detection performance. Its performance is compared with RBF kernels under a standard kernel PCA framework and with other methods proposed for multimode process monitoring via numerical examples. Moreover, a benchmark data set collected from a pilot-scale multiphase flow facility is used to demonstrate the advantages of the new kernel when applied to an experimental data set.