Numerical simulations and scaling arguments are used to study the field dependence of a random walk in a one-dimensional system with a bias field on each site. The bias is taken randomly with equal probability to be +E or −E. The probability density¯P(x, t) is found to scale asymptotically as $$\left\{ {[A(E)]^{\beta /2} /\ln ^2 t} \right\}\exp \left( { - \left\{ {x[A(E)]^{\beta /2} /\ln ^2 t} \right\}^\alpha } \right)$$ withA(E)=ln[(1+E)/(1-E)],β=4.25, and α=1.25. The mean square displacement scales as\(\langle x^2 \rangle \sim [A(E)]^{ - \beta } F[tA^\beta (E)]\), where F(u)∼ln4u asymptotically.