Solihull Metropolitan Borough Council is set to install two points outside Council House in the town centre.
It would cost the authority £8,000 to install, about £300 a year to maintain and about a pound per charge.
Drivers would pay for parking but not electricity under the plans, being considered today by Solihull Metropolitan Borough Council.
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Nearest other points are in Birmingham and Leamington Spa.
A report said: “To facilitate expansion in use of electric vehicles it is essential that a network of charging points is developed.
“Without this people are less likely to consider the purchase of an electric vehicle as an option. With projects being delivered in Birmingham, Coventry and Leamington,
“Solihull is ideally placed as a mid commuting point to extend the range of travel for existing electric vehicle owners.”