Information on the availability of parking spaces is needed for drivers. Drivers walking around looking for parking spaces have negative impacts, including traffic jams, waste of fuel, increasing pollution and even causing driver panic. Classification of parking spaces properly and quickly becomes a solution to present information on the availability of parking spaces. Based on the technology used, parking space classification usually uses sensors or computer vision. However, computer vision is lower in cost usage because a single camera can classify multiple parking spaces simultaneously. Convolutional Neural Network (CNN) is a popular method in dealing with vision problems. mAlexnet is one of the CNN architectures that has succeeded in classifying parking spaces well, but its accuracy still needs to be improved. A better architecture of mAlexnet needs to be made to improve classification accuracy and speed. In this study, we designed a CNN architecture named ParkingNet. Based on testing using sub-dataset camera B from the CNRPark dataset, ParkingNet is better than mAlexnet, both in terms of accuracy, the number of parameters, and FLOPs. ParkingNet managed to outperform mAlexnet's accuracy by 0.68%. Although not significant, ParkingNet is faster in classification due to the smaller number of parameters and FLOPs. The number of ParkingNet parameters is 4/5 mAlexnet parameters and the number of ParkingNet FLOPs is 2/5 mAlexnet. ParkingNet can be implemented in a smart parking system to classify parking spaces with lower computational costs.