Can you qualify for a British passport if your mother is a British passport holder born in Zimbabwe and your grandfather is a British passport holder born in the UK?

Call the responsible authorities and ask. If you are in countries other than the UK, contact the nearest British High Commission.

Answer

It depends on individual circumstances. Ancestry is unlikely to be a decisive factor if you are substantially Zimbabwean. You may have to live in the UK for a few years first then apply to become a British Nationalised Citizen.