We propose a fusion network model for handwriting recognition. The model consists of a feedforward fully connected neural network (FNN) and a convolutional neural network (CNN). For a given handwriting trajectory, we generate two types of inputs for the FNN and CNN networks, respectively. Each of the networks produces a confidence vector for a handwriting trajectory. Subsequently, the fused result is the element-wise product of the two confidence vectors. We evaluated the proposed fusion network on two data sets, namely RTD and 6DMG, which contain alphabetic and numeric handwriting data. Five-fold cross validation was adopted. The average accuracy of our fusion network achieved 99.77% on the alphabetic data and 99.83% on the numeric data of the 6DMG data set, and 99.61% on the RTD data set. Finally, we compared the fusion network with three state-of-the-art techniques.