During the first part of life, the brain develops while it learns through a process called synaptogenesis. The neurons, growing and interacting with each other, create synapses. However, eventually the brain prunes those synapses. While previous work focused on learning and pruning independently, in this work we propose a biologically plausible model that, thanks to a combination of Hebbian learning and pruning, aims to simulate the synaptogenesis process. In this way, while learning how to solve the task, the agent translates its experience into a particular network structure. Namely, the network structure builds itself during the execution of the task. We call this approach Self-building Neural Network (SBNN). We compare our proposed SBNN with traditional neural networks (NNs) over three classical control tasks from OpenAI. The results show that our model performs generally better than traditional NNs. Moreover, we observe that the performance decay while increasing the pruning rate is smaller in our model than with NNs. Finally, we perform a validation test, testing the models over tasks unseen during the learning phase. In this case, the results show that SBNNs can adapt to new tasks better than the traditional NNs, especially when over $80\%$ of the weights are pruned.