The single kernel total projection to latent structures (T-PLS) would lead to a higher missing alarm rate and false alarm rate because either global kernel function or local kernel function can be utilized. The hybrid kernel T-PLS algorithm proposed in this paper combines global function with local function to solve nonlinear problems by projecting low-dimensional input data to high-dimensional feature space. The feature space is then divided into output directly correlated subspace, output orthogonal subspace, output uncorrelated subspace, and residual subspace by output variables. Based on fault detected by statistic D and Q in these subspaces, respectively, fault-free data are reconstructed and the fault magnitude is estimated by generalized reconstruction-based contribution (RBC). The simulation results of Tennessee Eastman process show the proposed algorithm can not only detect output-relevant fault with higher detection rate, but also identify the type of fault.