Given n data points in d-dimensional space, k nearest neighbors searching involves determining k nearest of these data points to a given query point. A depth-first adaptive kNN searching (DAKNNs) algorithm is proposed. The algorithm finds k nearest neighbors of the query point in a small hyperball in order to improve the efficiencies. It firstly determines the minimal radius rmin of the hyperball according to the rules, and then estimates the effective radius reffective of other points' hyperball. With the algorithm, the cost to find k nearest neighbors of one point is O(alphad)(1 les alpha Lt n),and the cost of preprocessing is O(dnlog2n). Our experiment shows the algorithm performance is superior to other known algorithms