For many purposes (e.g., satellite drag, operation of power grids on Earth, and satellite communication systems), predictions of the strength of a solar cycle are needed. Predictions are made by using different methods, depending upon the characteristics of sunspot cycles. However, the method most successful seems to be the precursor method by Ohl and his group, in which the geomagnetic activity in the declining phase of a sunspot cycle is found to be well correlated with the sunspot maximum of the next cycle. In the present communication, the method is illustrated by plotting the 12-month running means aa(min) of the geomagnetic disturbance index aa near sunspot minimum versus the 12-month running means of the sunspot number Rz near sunspot maximum [aa(min) versus Rz(max)], using data for sunspot cycles 9 -18 to predict the Rz(max) of cycle 19, using data for cycles 9 -19 to predict Rz(max) of cycle 20, and so on, and finally using data for cycles 9 -23 to predict Rz(max) of cycle 24, which is expected to occur in 2011 -2012. The correlations were good (∼+0.90) and our preliminary predicted Rz(max) for cycle 24 is 142 ± 24, though this can be regarded as an upper limit, since there are indications that solar minimum may occur as late as March 2008. (Some workers have reported that the aa values before 1957 would have an error of 3 nT; if true, the revised estimate would be 124 ± 26.) This result of the precursor method is compared with several other predictions of cycle 24, which are in a very wide range (50 -200), so that whatever may be the final observed value, some method or other will be discredited, as happened in the case of cycle 23.