The mobility of electrons in vertical transport in GaAs/Ga(1-y)Al(y)As barrier structures was investigated using geometric magnetoresistance measurements in the dark. The samples studied had Ga(1-y)Al(y)As (0 <= y <= 0:26) linearly graded barriers between the n(+)-GaAs contacts and the Ga(0:74)Al(0:26)As central barrier, which contain N(w) (=0, 2, 4, 7 and 10) n-doped GaAs quantum wells. The mobility was determined as functions of (i) temperature (80-290 K) at low applied voltage (0.01-0.1 V) and (ii) applied voltage (0.005-1.6 V) at selected temperatures in the range 3.5-290 K. The experimental results for the temperature dependence of low-field mobility suggest that space-charge scattering is dominant in the samples with N(w) =0 and 2, whereas ionized impurity scattering is dominant in the samples with N(w) =4, 7 and 10. The effect of polar optical phonon scattering on the mobility becomes significant in all barrier structures at temperatures above about 200 K. The difference between the measured mobility and the calculated total mobility in the samples with N(w) =4, 7 and 10, observed above 200 K, is attributed to the reflection of electrons from well-barrier interfaces in the quantum wells and interface roughness scattering. The rapid decrease of mobility with applied voltage at high voltages is explained by intervalley scattering of hot electrons.