This work investigates the problem of detecting gravitational wave (GW) events based on simulated damped sinusoid signals contaminated with white Gaussian noise. It is treated as a classification problem with one class for the interesting events. The proposed scheme consists of the following two successive steps: decomposing the data using a wavelet packet, representing the GW signal and noise using the derived decomposition coefficients; and determining the existence of any GW event using a convolutional neural network (CNN) with a logistic regression output layer. The characteristic of this work is its comprehensive investigations on CNN structure, detection window width, data resolution, wavelet packet decomposition and detection window overlap scheme. Extensive simulation experiments show excellent performances for reliable detection of signals with a range of GW model parameters and signal-to-noise ratios. While we use a simple waveform model in this study, we expect the method to be particularly valuable when the potential GW shapes are too complex to be characterized with a template bank.