This paper experimentally evaluates the effect of slope on spread of a linear flame front over a pine needle fuel bed in still air. The slope angle of the fuel bed varied from 0 to 32°. The fuel mass consumption in flaming fire spread, temperature over the fuel bed, velocities of the flow around the flame front and heat fluxes (total and radiant) near the end of the fuel bed were measured. The mass loss rate and rate of fire spread both increased with increasing slope, whereas the fuel consumption efficiency varied in the opposite way. It was shown that a weak reverse inflow and an upslope wind (induced by the flame itself) exist respectively ahead of and behind the flame front, and their significant difference in velocity (causing a pressure difference) plays an essential role in the forward tilting of the flame front. This mechanism promotes burning, especially on higher slopes. Natural convective cooling has a remarkable effect on the fuel pre-heating in the spread of linear flame fronts under slope conditions. A fire spread model for a linear flame front was developed to consider the natural convective cooling and the fuel consumption efficiency. The model agrees well with the experimental data on fire spread rate. Its reliability, especially for higher slopes, was verified by comparison with other models.