This paper presents a level set boundary description (LSBD) approach for novelty detection that treats the nonlinear boundary directly in the input space. The proposed approach consists of level set function (LSF) construction, boundary evolution, and termination of the training process. It employs kernel density estimation to construct the LSF of the initial boundary for the training data set. Then, a sign of the LSF-based algorithm is proposed to evolve the boundary and make it fit more tightly in the data distribution. The training process terminates when an expected fraction of rejected normal data is reached. The evolution process utilizes the signs of the LSF values at all training data points to decide whether to expand or shrink the boundary. Extensive experiments are conducted on benchmark data sets to evaluate the proposed LSBD method and compare it against four representative novelty detection methods. The experimental results demonstrate that the novelty detector modeled with the proposed LSBD can effectively detect anomalies.