Social networking sites like Twitter, Facebook, Google + are rapidly gaining popularity as they allow people to share and express their views about topics, have discussion with different communities, or post messages across the world. There has been a lot of work in the field of sentiment analysis of Twitter data. Randomization based methods for training neural networks have gained increased attention in recent years achieving remarkable performances on a wide variety of tasks. The idea of randomly assigning neural network parameters is shared by different models like Random Vector Functional Link (RVFL) networks, the Liquid State Machine and the Feedforward Neural Network with Random Weights. We propose a novel non-iterative deep neural network using RVFL networks called Deep RVFL (D-RVFL). We evaluate the performance of D-RVFL using two Twitter datasets (the Catalan referendum of 2017 and the Chilean earthquake of 2010). In particular, we compare the classification performance of D-RVFL in human sentiment with Support Vector Machine (SVM), Random Forest, and the standard RVFL. The results confirm the advantages of using the proposed method for sentiment classification in Twitter in terms of the F1 score.