With the advancement of emerging power-to-gas (P2G) technologies, the integrated power and gas distribution system (IPGDS) with bidirectional energy conversion is becoming a promising measure to promote the integration of renewablebased distributed generation. This study proposes the linear network model for the IPGDS and takes the reactive power consumption of P2G into account. The linear model considering the network constraints of the IPGDS is implemented combining the Wendroff difference for gas network equations and the pyramidal approximation for power network equations. With the proposed linear network model, the economic dispatch of the IPGDS is studied considering distribution network reconfiguration. Both the overall positive role of P2G and the negative effect of P2G's reactive power consumption are analysed. The former helps to mitigate the voltage violations and to improve economic efficiency, while the latter reduces these benefits. Case studies in the integrated 33-bus power and 12-node gas distribution system validate the effectiveness and applicability of the proposed linear network model of the IPGDS and the necessity of considering P2G's reactive power consumption. β switch status, binary, 0/1 for open/closed switches P sub * auxiliary variable, purchased power P L * auxiliary variable, active power flow