Strontium cobalt oxides attract great research attention because of their potential applications in electronic, magnetic, and energy devices. Despite the good crystalline quality of thin films made by pulsed laser deposition or molecular beam epitaxy, the surface properties, such as surface reconstructions and electronic and spintronic properties of surfaces, are complex and largely unknown. This is probably due to the relatively complexed crystal structure with internal oxygen vacancy channels and relatively low quality of surface morphology. A powerful theoretical guideline of the electron counting model has been proved to be effective in surface studies, yet the applicability of the model to complexed thin film structures is also unknown. Also, this model is based on electron transfers among surface atoms and may be inefficient for complexed electron transfer among the top surface and internal surfaces. In this work, we compute the phase diagram and surface formation energy based on density functional theory (DFT). To quickly search for the most stable surface configurations, we propose a new approach to count the electron shortages and electron supplies based on each layer, which is ideal for complexed electron-transfer phenomena. Based on this new approach, we discover the most stable surface configuration and proper passivation schemes. The stability of our proposed structure is confirmed by the DFT calculations. Based on the most stable structure, we discover an interesting coupling mechanism between the surface states and the magnetism by introducing different concentrations of H on the top surface and found that both surface conductivities and magnetic properties are strongly influenced by the H. Our finding sheds light to the understanding of interplay between surface states and bulk magnetism in transition-metal oxides.