Slug flow is one of the most common flow patterns that occur during flow boiling in horizontal micro-channels. In the present work, an analytical model of flow boiling heat transfer is developed for slug flow in a single circular horizontal micro-channel under a uniform heat flux. The heat transfer is affected mainly by the liquid film thickness confined between the vapor slug and the channel wall. For more physical and reliable flow boiling heat transfer model, the liquid film thickness variation and pressure gradient effects on the flow boiling heat transfer coefficient are considered. The influence of vapor quality on heat transfer coefficient, vapor velocity and liquid film velocity is studied. The model is constructed based on the conservation equations of the separated two phase flow. The interphase surface is assumed to be smooth and the flow is a laminar flow. The obtained model applied for flow boiling of R-134a refrigerant in the slug flow at a narrow vapor quality range (0.0 < x < 0.1). The heat transfer coefficient showed a high increase close to the low vapor quality while decreases gradually after the peak. Furthermore, the vapor velocity increases linearly by increasing the vapor quality while, the liquid film velocity decreases.