Statistical parametric speech synthesis (SPSS) using deep neural networks (DNNs) has shown its potential to produce naturally-sounding synthesized speech. However, there are limitations in the current implementation of DNN-based acoustic modeling for speech synthesis, such as the unimodal nature of its objective function and its lack of ability to predict variances. To address these limitations, this paper investigates the use of a mixture density output layer. It can estimate full probability density functions over real-valued output features conditioned on the corresponding input features. Experimental results in objective and subjective evaluations show that the use of the mixture density output layer improves the prediction accuracy of acoustic features and the naturalness of the synthesized speech.