Magnitude of an earthquake is an important measure used to compare earthquakes in space and time.There are some problems with the current magnitude scales，ML，MS，mB and mb，including uncertainty in the physical meaning and determination results are inconsistent.It is widely recognized that the moment magnitude is an absolute standard measurement of mechanics and may be an ideal magnitude scale because it is not a magnitude of saturation but stabilization.This article briefly demonstrates some progress achieved by Chinese scholars in comparing disparate magnitude scales used by the China Earthquake Networks Center （CENC） and major foreign organizations.In addition，conversional relationships between various earthquake magnitude scales are explored.We will present the comparison between the moment magnitudes for various earthquake magnitude scales and foreign standards，for example，when 6.5≤M≤7.6，mB≈MW；when 5.2≤M≤8.0，MS≈MW；when 4.2≤M≤7.0，ML≈MW；when 4.0≤M≤6.0，and mb≈MW. In each range above，the deviation between MW and mB，and between ML andMS is less than or equal to 0.2. After derivation，the comparison of moment magnitudes and earthquake magnitude scales in our regular standards are as follows：when 4.5≤M≤5.8，mB≈MW；when 4.5≤M≤7.5，mb≈MW；when 4.5≤M≤7.0，ML≈MW；And MS≈MW；MS7=MW.In the magnitude ranges above，MW deviated from mb and MS by less than or equal to 0.2，was equal to MS7；and deviated from ML by 0.22. It is suitable for all kinds of magnitude scale ranges，whereby generally：ML is applied to magnitude 1.0~5.9 earthquakes；mB is applied to magnitude 3.5~6.5 earthquakes；mB is applied to magnitude 4.5~7.5 earthquakes；MS is applied to magnitude 6.0~8.0 earthquakes; and MW is applied to all earthquake magnitudes.It is also considered a priority to catalogue conversions from the different magnitude scales.The process of earthquake rupture is complicated，between the same rupture scales （the same M0），and the altitude source spectra of some frequency are very different because of the different stress field background，rupture velocity，and rupture pattern.It is shown that there is a big difference between magnitude scales because of the limit used by different countries，different geographical conditions， instrumentation，and formula for computing magnitude.The conversion relationship between different magnitude scales is difficult to define.This article showed that the conversion formula of moment magnitude was inferred further using empirical formulas based on prior studies and not direct conversion between moment magnitude and other magnitude scales. The approach used here could be applied to earthquake forecasting.The next step to carry out the work is that establishing direct experience relation according to the thought from Mr.Chen Peisheng: establishing direct relation formula between ML，MS，mB，mb，and MW so the results may be more reliable.In addition，it would be necessary to investigate a number of parameters such as seismic moment of great earthquake，small earthquake，shallow （-focus） earthquake，and bathyseism.Seeking empirical relationships between logs M0，ML，MS， and mb is a good approach.