Motivated by the growing demand for distributed energy resources (DERs), peer-to-peer (P2P) electricity markets have been explored worldwide. However, such P2P markets must be balanced in much smaller regions with a lot fewer participants than centralized wholesale electricity markets; hence, the market has inherent problems of low liquidity and price instability. In this study, we propose applying a market maker system to the P2P electricity market and developing an efficient market strategy to increase liquidity and mitigate extreme price fluctuations. To this end, we construct an artificial market simulator for P2P electricity trading and design a market agent and general agents (photovoltaic (PV) generators, consumers, and prosumers) to perform power bidding and contract processing. Moreover, we introduce market-maker agents in this study who follow the regulations set by a market administrator and simultaneously place both sell and buy orders in the same market. We implement two types of bidding strategies for market makers and examine their effects on liquidity improvement and price stabilization as well as profitability, using solar PV generation and consumption data observed in a past demonstration project. It is confirmed that liquidity and price stability may be improved by introducing a market maker although there is a trade-off relationship between these effects and the market maker’s profitability.