In this work, the electronic properties of phosphorene nanoribbons with different width and edge configurations are studied by using density functional theory. It is found that the armchair phosphorene nanoribbons are semiconducting while the zigzag nanoribbons are metallic. The band gaps of armchair nanoribbons decrease monotonically with increasing ribbon width. By passivating the edge phosphorus atoms with hydrogen, the zigzag series also become semiconducting, while the armchair series exhibit a larger band gap than their pristine counterpart. The electronic transport properties of these phosphorene nanoribbons are then investigated using Boltzmann theory and relaxation time approximation. We find that all the semiconducting nanoribbons exhibit very large values of Seebeck coefficient and can be further enhanced by hydrogen passivation at the edge. Taking pristine armchair nanoribbons and hydrogen-passivated zigzag naoribbons with width N = 7, 8, 9 as examples, we calculate the lattice thermal conductivity with the help of phonon Boltzmann transport equation and evaluate the width-dependent thermoelectric performance. Due to significantly enhanced Seebeck coefficient and decreased thermal conductivity, we find that at least one type of phosphorene nanoribbons can be optimized to exhibit very high figure of merit (ZT values) at room temperature, which suggests their appealing thermoelectric applications.