Abstract: The volatility of asset prices is an important research topic that scholars pay close attention to. In recent years, scholars have proposed many estimation methods for volatility, and studied the consistency and asymptotic normality of the estimators. In this paper, we focuses on the NW type kernel estimator of spot volatility proposed by Kristensen\ucite26, points out that there are some errors in the relevant proof process, and derives further the strong consistency and uniform strong consistency of the estimator under some reasonable conditions.