Early detection of Alzheimer's Disease (AD) is greatly beneficial to AD patients, leading to early treatments that lessen symptoms and alleviating financial burden of health care. As one of the leading signs of AD, language capability changes can be used for early diagnosis of AD. In this paper, I develop a robust classification method using hybrid word embedding and fine-tuned hyperparameters to achieve state-of-the-art accuracy in the early detection of AD. Specifically, we create a hybrid word embedding based on word vectors from Doc2Vec and ELMo to obtain perplexity scores of the sentences. The scores identify whether a sentence is fluent or not and capture semantic context of the sentences. I enrich the word embedding by adding linguistic features to analyze syntax and semantics. Further, we input an embedded feature vector into logistic regression and fine tune hyperparameters throughout the pipeline. By tuning hyperparameters of the machine learning pipeline (e.g., model regularization parameter, learning rate and vector size of Doc2Vec, and vector size of ELMo), I achieve 91% classification accuracy and an Area Under the Curve (AUC) of 97% in distinguishing early AD from healthy subjects. Based on my knowledge, my model with 91% accuracy and 97% AUC outperforms the best existing NLP model for AD diagnosis with an accuracy of 88% [32]. I study the model stability through repeated experiments and find that the model is stable even though the training data is split randomly (standard deviation of accuracy = 0.0403; standard deviation of AUC = 0.0174). This affirms our proposed method is accurate and stable. This model can be used as a large-scale screening method for AD, as well as a complementary examination for doctors to detect AD.