Relation classification is an important research arena in the field of natural language processing (NLP). In this paper, we present SDP-LSTM, a novel neural network to classify the relation of two entities in a sentence. Our neural architecture leverages the shortest dependency path (SDP) between two entities; multichannel recurrent neural networks, with long short term memory (LSTM) units, pick up heterogeneous information along the SDP. Our proposed model has several distinct features: (1) The shortest dependency paths retain most relevant information (to relation classification), while eliminating irrelevant words in the sentence. (2) The multichannel LSTM networks allow effective information integration from heterogeneous sources over the dependency paths. (3) A customized dropout strategy regularizes the neural network to alleviate overfitting. We test our model on the SemEval 2010 relation classification task, and achieve an $F_1$F1​-score of 83.7%, higher than competing methods in the literature.