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With the joint optimization of the electricity–gas–heating system (EGHS) attracting more and more attention, a distributed optimized scheduling framework for EGHS based on an improved alternating direction method of multipliers (ADMM) algorithm is put forward in this paper. The framework of the proposed algorithm is a co-ordinated convex distribution framework with inner and outer layers. The outer layer is a penalty convex–concave procedure (PCCP), the inner layer is an ADMM-FE (forced equality) procedure. In this framework, the outer layer optimization uses the convex and concave procedure to turn the non-convex airflow equation into a second-order cone constraint with successive iterations, and the inner layer ADMM-FE algorithm solves the convex model to obtain a convergent solution. In the end, we compare the established algorithm with the traditional ADMM algorithm and the centralized optimization algorithm through example simulation analysis, and the results verify the effectiveness of the proposed model and optimization algorithm framework.