The maximum of a solar cycle contain two or more peaks, known as Gnevyshev peaks. Studies of this property of solar cycles may help for better understanding the solar dynamo mechanism. We analysed the 13-month smoothed monthly mean Version-2 international sunspot number (SN) during the period 1874–2017 and found that there exists a good correlation between the amplitude (value of the main and highest peak) and the value of the second maximum (value of the second highest peak) during the maximum of a solar cycle. Using this relationship and the earlier predicted value 86 ± 18 (92 ± 11) of the amplitude of Solar Cycle 25, here we predict a value 73 ± 15 (79 ± 15) for the second maximum of Solar Cycle 25. The ratio of the predicted second maximum to the amplitude is found to be 0.85, almost the same as that of Solar Cycle 24. The least-square cosine fits to the values of the peaks that occurred first and second during the maxima of Solar Cycles 12–24 suggest that in Solar Cycle 25 the second maximum would occur before the main maximum, the same as in Solar Cycle 24. However, these fits suggest ≈106 and ≈119 for the second maximum and the amplitude of Solar Cycle 25, respectively. Earlier, we analysed the combined Greenwich and Debrecen sunspot-group data during 1874–2017 and predicted the amplitude of Solar Cycle 25 from the activity just after the maximum of Solar Cycle 24 in the equatorial latitudes of the Sun’s southern hemisphere. Here from the hindsight of the results we found the earlier prediction is reasonably reliable. We analysed the polar-fields data measured in Wilcox Observatory during Solar Cycles 20–24 and obtained a value 125 ± 7 for the amplitude of Solar Cycle 25. This is slightly larger–whereas the value ≈86 (≈92) predicted from the activity in the equatorial latitudes is slightly smaller–than the observed amplitude of Solar Cycle 24. This difference is discussed briefly.