When we work with Tab file in Mapinfo we can save the style directly into the Tab file.
Is there any way to save a feature layer together with a defined style into tab file in QGIS?
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The way that MapInfo's styling works is unusual, in that it is per-feature.
The only way you're going to be able to do it is if you implement a plugin yourself, and it'll be fiddly, as you'll need to consider what styles are supported by MapInfo, and also implement a lookup table between MapInfo's odd numbering style for patterns and their weird colour storage method.
The short answer is that, you can't easily store MapInfo styles with QGIS.
A way I've gotten around this is using FME to process features and automatically add MI styles (this was in an SQL Server database).
Alternately, you could maintain a list of strings that are common MapInfo styles, and maintain them as attributes. (Assuming again you're working with a database table, and can edit the MI_STYLE attribute manually.)