In order to clarify the apparent discrepancy in determinations of melting temperature Tm of Mo between diamond-anvil cell (DAC) measurements from 0 to about 100 Gpa and shock wave (SW) measurement at only one pressure of about 390 Gpa by comparison with visual extrapolation, we perform SW experiments to replenish more Tm data on purpose to make this comparison more directly and rationally as well. The techniques adopted consist of Hügoniot sound velocity measurement for porous Mo and shock-induced release Tm measurements for both solid and porous Mo. Totally five SW Tm data, which extends the measured pressure range from previous about 390 Gpa down to about 136 Gpa that is close to the highest pressure (about 100 Gpa) attained by previous DAC experiments, are therefore obtained. These measured Tm data, other than the extrapolated as mentioned above, exhibit a manner of continuous variation with pressure and can be fitted well with Lindemann melting description. More significantly, the measured Tm data at lowest pressure are still much higher than that of the DACs and the overall trend of these Tm data is against to the two-segment melting curve model, with a sudden change in dTm/dp at about 210 Gpa, previously proposed by Errandonea [Physica B 357 (2005) 356]. Though the problem of large discrepancy in Tm data measured between DAC and SW has not been completely explained, our knowledge on this matter achieves indubitable progress since it is of value to programme the next clarification. Some suggestions for further clarifying the issue of large discrepancy between DAC and SW measurements are also proposed.