With the development of wireless sensor networks (WSNs), WSNs have been widely used in various fields such as animal habitat detection, military surveillance, etc. This paper focuses on protecting the source location privacy (SLP) in WSNs. Existing algorithms perform poorly in non-uniform networks which are common in reality. In order to address the performance degradation problem of existing algorithms in non-uniform networks, this paper proposes a robust fixed path-based random routing scheme (RFRR), which guarantees the path diversity with certainty in non-uniform networks. In RFRR, the data packets are sent by selecting a routing path that is highly differentiated from each other, which effectively protects SLP and resists the backtracking attack. The experimental results show that RFRR increases the difficulty of the backtracking attack while safekeeping the balance between security and energy consumption.