Human inertial navigation systems have been developing rapidly in recent years, and it has shown great potential for applications within healthcare, smart homes, sports, and emergency services. Placing inertial measurement units on the head for localisation is relatively new. However, it provides a very interesting option, as there are several everyday head-worn items that could easily be equipped with sensors. Yet, there remains a lack of research in this area and currently no localisation solutions have been offered that allow for free head-rotations during long periods of walking. To solve this problem, we present HINNet, the first deep neural network (DNN) pedestrian inertial navigation system allowing free head movements with head-mounted inertial measurement units (IMUs), which deploys a 2-layer bi-directional LSTM. A new ’peak ratio’ feature is introduced and utilised as part of the input to the neural network. This information can be leveraged to solve the issue of differentiating between changes in movements related to the head and those that are associated with the walking pattern. A dataset with 8 subjects totalling 528 min has been collected on three different tracks for training and verification. The HINNet could effectively distinguish head rotations and changes in walking direction with a distance percentage error of 0.46%, a relative trajectory error of 3.88 m, and a absolute trajectory error of 5.98 m, which outperforms the current best head-mounted Pedestrian Dead Reckoning (PDR) method.