Abstract: Let X be a d-dimensional random vector with unknown density function f(z)=f(z₁,…, z_d), and let f_n be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f_n for general case of d ≥ 1, which gives the exact pointwise strong convergence rate of f_n.