Summary: This paper considers a \(\lambda\)-biased random walk on Galton-Watson trees. It is proved that the speed exists and is bounded above by \((m \lambda)/(m+\lambda)\), where \(m\) is the mean of offsprings. We further explore the relation between the speed and the offspring distribution. All examples show that the speed is a monotone function of the variance. We confirm this belief by verifying that the recurrent probability, a quantity related to the speed, is a monotone function of the variance of the offspring distribution in some sense, for the fixed \(m\). Some observations are made and some questions are raised.