We present here, the results of an investigation on giant magnetoimpedance (GMI) effect in both annealed and as-quenched Co70Fe5Si15B10 and Co70Fe5Si15Nb2.2Cu0.8B7 ribbons. Substitution of Cu and Nb for B in an initial Co70Fe5Si15B10 composition forming the Co70Fe5Si15Nb2.2Cu0.8B7 composition improves both GMI effect and its field sensitivity. The GMI effect was more pronounced in the annealed samples. The field sensitivity of both the longitudinal permeability ratio and the magnetoimpedance ratio for the annealed Co70Fe5Si15Nb2.2Cu0.8B7 ribbon increase exponentially as the testing temperature is increased, indicating that the magnetic permeability is very sensitive to the temperature. The results obtained are of significant importance in developing quick-response magnetic sensors.