Recent measurements of an unusual high thermal conductivity of around 1000 W m-1 K-1 at room temperature in cubic boron arsenide (BAs) confirm predictions from theory and suggest potential applications of this semiconductor compound for thermal management applications. Knowledge of the thermal expansion coefficient and Gruneisen parameter of a material contributes both to the fundamental understanding of its lattice anharmonicity and to assessing its utility as a thermal-management material. However, previous theoretical calculations of the thermal expansion coefficient and Gruneisen parameter of BAs yield inconsistent results. Here we report the linear thermal expansion coefficient of BAs obtained from the X-ray diffraction measurements from 300 K to 773 K. The measurement results are in good agreement with our ab initio calculations that account for atomic interactions up to fifth nearest neighbours. With the measured thermal expansion coefficient and specific heat, a Gruneisen parameter of BAs of 0.84 +/- 0.09 is obtained at 300 K, in excellent agreement with the value of 0.82 calculated from first principles and much lower than prior theoretical results. Our results confirm that BAs exhibits a better thermal expansion coefficient match with commonly used semiconductors than other high-thermal conductivity materials such as diamond and cubic boron nitride.