Electrochemical impedance spectroscopy (EIS) is a widely used technique to measure macroscopic properties of electrodes. However, the underlying connections between the obtained macroscopic properties and electrode microstructures are not well understood because of the complexity of coupled electrochemical mechanisms and microstructure morphology. In this work, we present a smoothed-boundary-method (SBM) electrochemical simulation framework to directly simulate the electrochemical dynamics with explicit consideration of electrode microstructures and extract EIS curves from the electrochemical simulations. This method uses continuous domain parameters to define the complex geometries of electrode particles and electrolyte phase in the interparticle space, thus circumventing the requirement of mesh conforming to the complex electrode microstructures in the simulations. The SBM is also utilized to calculate the double-layer capacitance that is required in the physics-based EIS simulations. The effects of the state of charge, salt concentration in electrolyte, and particle size distribution in electrode on the resulting EIS curves are examined using the SBM simulations. This simulation tool allows us to accessibly reveal the underlying connections between intrinsic material properties, microstructures, and macroscopic EIS measurements of battery electrodes.