We are planning to rent a car in Santiago de Compostela and drive through Portugal retuning the car in Lisbon and from here take the bus to Seville.
I would like to know if it is possible.

It's certainly possible. There will probably be a sizeable drop off fee for doing so.

I would shop around among the various companies to see who has the best deal taking the drop off fee into account.

Do they charge more insurance for using the car in two country?

I'd just keep the car and return it in Seville. No drop-off charge and extra day/fuel will probably come to less than bus fares. Lisbon-Seville is only around 285 miles by motorway or 250 miles by more direct route.

Thank you for the replies. I do plan all our trips by reading some of the Fodor’s trip reports posted here.
We want to stay in Lisbon for at least 3 days and the more I read in this forum the more I feel that it is not a good idea to keep a car in there, beside that we will not use the car during our stay in Lisbon and we will need to find a place to park it.
But I am open to suggestions and maybe will be cheaper and more pleasant to drive to Seville. Any special route and stops along that is worth taken if we decide to keep the car?