This paper introduces a kernel adaptive filter using the stochastic gradient on temporal differences, kernel TD(λ), to estimate the state-action value function Q in reinforcement learning. Kernel methods are powerful for solving nonlinear problems, but the growing computational complexity and memory size limit their applicability on practical scenarios. To overcome this, the quantization approach introduced in  is applied. To help understand the behavior and illustrate the role of the parameters, we apply the algorithm on a 2-dimentional spatial navigation task. Eligibility traces are commonly applied in TD learning to improve data efficiency, so the relations of eligibility trace λ and step size and filter size are observed. Moreover, kernel TD (0) is applied to neural decoding of an 8 target center-out reaching task performed by a monkey. Results show the method can effectively learn the brain-state action mapping for this task.