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Central Trains has applied for planning permission for the single storey car park deck from Solihull Metropolitan Borough Council.
It would add 186 spaces, giving a total 466 spaces.
It has also applied for a temporary car park at nearby Tudor Grange Swimming Pool, on land next to existing spaces to the back left of the site.
The train company said track improvements set to cut journey times from Solihull to London by half-an-hour to an hour and 22 minutes would increase demand by 20 per cent, to 1,900 return journeys every weekday.
It said: "If the additional car parking capacity is not provided, it is however very likely that the majority of those car users who are unable to park at the station will drive to a more distant railway station with sufficient parking capacity, or will complete their entire journey by private car."
To see the applications click here and enter 2011 and 491 or 495 in the two boxes.
The council is expected to make a decision by the end of May.
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