Relative colour strength (RCS) of dye plays an important role in the production, the evaluation and the application of dyes. There are different standards on the determination of it, their principles are all related to colour depth. However, the standard methods have some limitations. For this purpose, this study proposed a new method for the RCS based on the new colour depth formula Yangn, which included three methods named colour strength value (CSV1, CSV2 and CSV3). Part I in this study was to investigate the application effect of Yangn on the RCS of different disperse dyes with approximate hues. According to the experimental results of E-type and SE-type disperse dyes, the new method showed its advantages. Firstly, compared with AATCC EP-6, the results of the new method were more consistent. Secondly, under different dyeing concentrations, the RCS values of the new method were relatively consistent, with average coefficient values (CVs) being less than 5%, especially for CSV3 with only 3.59%; while all the average CVs of AATCC EP-6 were greater than 6%. For the calculation of RCS of different types of dyes with approximate hue, the new method presented more accurate results.