Differential Privacy (DP) is commonly employed to safeguard graph analysis or publishing. Distance, a critical factor in graph analysis, is typically handled using curator DP, where a trusted curator holds the complete neighbor lists of all vertices and answers queries privately. However, in many real-world scenarios, such a curator may not be present, posing a significant challenge for implementing differentially private distance queries under Local Differential Privacy (LDP). This paper proposes two approaches to address this challenge. The first approach generates a synthetic graph by randomizing responses and applies bitwise operations to reduce noise interference. However, like other synthetic graph methods, this approach suffers from low utility. To overcome this limitation, we propose a second approach, the first LDP method specifically designed for distance queries, which captures the global graph structure by continuously aggregating local distance vectors from neighboring vertices. This process enables the accurate updating of global distances. We demonstrate the effectiveness of our method through comprehensive theoretical analysis and experimental evaluations on real-world datasets.