The N-gram model is one of the most commonly used language models in natural language processing and is widely used in many tasks such as speech recognition, handwriting recognition, spelling correction, machine translation and search engines. However, the N-gram model often presents zero-probability problems in training and application, resulting in failure to obtain a good language model. As a result, smoothing methods such as Laplace smoothing, Katz back-off, and Kneser-Ney smoothing appeared. After introducing the basic principles of these smoothing methods, we use the perplexity as a metric to compare the language models trained based on these types of smoothing methods.