Monetary policy is not only a policy tool to cope with sudden shocks and quickly realize economic recovery in the short term, but also has the effect of adjusting income distribution. By introducing heterogeneous household and monetary policy into the framework of dynamic stochastic general equilibrium analysis, this paper examines the distribution effects of expansionary monetary policy. Numerical simulations show that cutting interest rates not only boosts consumption and employment for ricardian and rule-of-thumb households, but also helps reduce consumption inequality and income inequality. Compared with the monetary policy rule without considering the factors of inequality, the extended rule that takes into account the consumption inequality and income inequality causes significantly lower social welfare losses. Therefore, when formulating and implementing monetary policy rules, not only household heterogeneity but also possible income and consumption inequalities should be taken into account.