Since the screening current (SC) in rare earth-barium-copper-oxide (REBCO) coated conductor (CC) generates an undesired magnetic field, it must be accurately estimated, especially for magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR). Moreover, in recent years, it was pointed out that the screening current enhanced the stress/strain in REBCO CC, when an REBCO magnet was operated as an insert under an ultrahigh magnetic field. The previously reported SC simulation methods may be roughly categorized into finite element method (FEM) and equivalent circuit method. The FEM-based method often adopted an axisymmetric model or a thin film approximation model, while the circuit-based are the simple equivalent circuit model and the network equivalent circuit model, so-called the partial element equivalent circuit model. The latter is newly proposed in this paper. Features of those SC simulation models are briefly compared to each other in this paper. Each SC simulation models have pros & cons. We have to adequately chose an SC simulation model depending on a purpose. In addition, we propose a new developed SC simulation model, named the advanced partial element equivalent circuit (A-PEEC) model. It is extendable to an SC simulation of no-insulation REBCO pancake coils. To simulate the SC of a simple coil model and the LBC3 magnet, we investigated the screening current distribution maps, and the simulated screening current-induced fields were compared with the measurements. We have confirmed the validity of the newly proposed A-PEEC model.