A continuum model of nanowires incorporating surface piezoelectricity is proposed which extends the electric enthalpy energy with surface terms. The corresponding equations are solved by a numerical method using finite elements technique. A methodology is introduced to compute the surface piezoelectric coefficients by first-principles calculations through the Berry phase theory. We provide the e^s_33; e_s^31, and e_s^15 piezoelectric coefficients of (10-10) surfaces for hexagonal wurtzite nanowires made of GaN, ZnO, and AlN. The effective piezoelectric coefficient along the axis of the nanowire is found to increase when the diameter decreases, for the three studied materials. Finally, the solution of the continuum model is compared with large-size first-principles calculations on piezoelectric nanowires.