In this paper, we present MobiEdit, a novel framework for knowledge editing of large-scale language models (LLMs) on mobile devices. Existing knowledge editing methods require resource-intensive backpropagation (BP), which makes them difficult to run on mobile devices. MobiEdit replaces backpropagation with forward-only quantized gradient estimation, thereby ensuring compatibility with energy-efficient mobile NPUs. In addition, we further improve the efficiency of gradient estimation by introducing an early stopping mechanism and a prefix cache. Experimental results show that MobiEdit enables real-time editing of a 3 billion-parameter model (Qwen2.5-3B-Instruct) with 7.6x less memory, 14.7x less energy, and 3.6x less latency compared to existing methods.