This paper proposed a Variable Length Codes (VLC) mapping-based Lossless Data Hiding (LDH) method that achieves stable file size increments in JPEG images. The study improves upon existing Reversible Data Hiding (RDH) techniques, which often result in unstable file size growth, especially in images with high texture complexity. The proposed method minimizes file size increments by reducing the number of VLC mappings and constructing a mapping relationship that ensures consistent file size growth across different embedding capacities. This approach effectively controls file size increments while preserving image visual quality and ensuring error-free decoding. Experimental results demonstrate that the proposed method offers better stability in controlling file size increments compared to previous VLC mapping-based LDH methods.