This paper describes a simple "multibox" model of the Arctic atmosphere-ice-ocean system. The model consists of two major modules (an Arctic module and a Greenland Sea module) and several sub-modules. The Arctic module includes a shelf box model coupled with a thermodynamic sea ice model, and an Arctic Ocean model coupled with a sea ice model and an atmospheric box model. The Greenland Sea module includes an oceanic model coupled with a sea ice model and a statistical model of surface air temperature over the Greenland Sea. The full model is forced by daily solar radiation, wind stress, river runoff, and Pacific Water inflow through Bering Strait. For validation purposes, results from model experiments reproducing seasonal variability of the major system parameters are analyzed and compared with observations and other models. The model reproduces the seasonal variability of the Arctic system reasonably well and is used to investigate decadal Arctic climate variability in part 2 of this publication (Dukhovskoy et al., 2006).