The orientation dependence of piezoresistivity in graphene nanoribbons has been discussed by carrying out the first-principles simulation. Our original procedure of simulating piezoresistive properties was applied to the one-dimensional nanoribbon systems in conductor state. For the armchair-oriented model series, band structures hardly change due to any strain, and the gauge factors are small as the common characteristics for the armchair-oriented graphene nanoribbons. On the other hand, various values of gauge factors have been obtained according to model size for the zigzag model series because of the nonuniformity of band structures among the model series. Generally, the zigzag model series have sufficiently large values of gauge factors for practical application to nanoscale piezoresistor. We have found the clear defference of gauge factors with respect to the orientation of graphene nanoribbon, and it is expected that zigzag-oriented graphene nanoribbons will have potential for use in future MEMS/NEMS technology.