Floating offshore wind turbine (FOWT) can harvest more wind energy in deep waters. However, due to the complex mechanical structures and harsh working conditions, various sensors, actuators, and components of FOWT can malfunction and fail. To avoid serious accidents and reduce operation and maintenance costs, fault detection plays a critical role in wind energy engineering, particularly for offshore wind energy. Because of the complex characteristics such as dynamics and nonlinearity, an accurate mathematical model can not be easily obtained from first principles for FOWT. In this paper, a new data-driven fault detection method based on kernel canonical variable analysis (KCVA) is proposed for FOWTs. In the proposed method, the collected measurements are first augmented into time-lagged variables to capture the dynamics of FOWT. Then, the time-lagged variables are mapped to a high-dimensional feature space to extract nonlinear features. Specifically, canonical variable analysis (CVA) is carried out to explore the correlations in high-dimensional feature space. For fault detection, two monitoring indexes, including $T^2$ and $SPE$ statistics are established. To verify the performance of the proposed KCVA based fault detection method, experiments on a high-fidelity FOWT benchmark, which was created from the National Renewable Energy Laboratory (NREL) FAST v8.0 simulator were carried out. Results show the capability and efficiency of the proposed KCVA-based fault detection method in comparison with other related methods.