With the use of first hand field survey data from 193 yak grazing households combined with remote sensing Net Primary Productivity data on the Qinghai-Tibetan Plateau, a directional output-orientation distance function is developed with four inputs, grassland area, labor, capital and initial livestock stocking, and two outputs, good output of livestock grazing revenue and undesirable output of grazing pressure. The average technical efficiency is estimated to be 0.82, and shadow price of grazing pressure to livestock revenue is estimated to be -1.8. According to Morishima elasticity of substitution between inputs, there is significant complementary relationship between grassland area, labor and capital. Elasticity of substitution between grassland and initial livestock stocking is estimated to be 0.50. Treating grazing pressure as an undesirable output of livestock grazing in the directional distance function is a new step in the general direction of better accounting for natural resource depletion in efficiency and production analysis.