This paper describes a neural network (NN) model that was used for participating in the OffensEval, Task 12 of the SemEval 2020 workshop. The aim of this task is to identify offensive speech in social media, particularly in tweets. The model we used, C-BiGRU, is composed of a Convolutional Neural Network (CNN) along with a bidirectional Recurrent Neural Network (RNN). A multidimensional numerical representation (embedding) for each of the words in the tweets that were used by the model were determined using fastText. This allowed for using a dataset of labeled tweets to train the model on detecting combinations of words that may convey an offensive meaning. This model was used in the sub-task A of the English, Turkish and Danish competitions of the workshop, achieving F1 scores of 90.88%, 76.76% and 76.70%, respectively.