This paper examines the potential and the cost of promoting forest carbon sequestration through a tax/subsidy to land owners for reducing/increasing carbon storage in their forests. We use a partial equilibrium model based on intertemporal optimization to estimate the impacts of carbon price (the tax/subsidy rate) on timber harvest volume and price in different time periods and on the change of forest carbon stock over time. The results show that a higher carbon price would lead to higher forest carbon stocks. The tax/subsidy induced annual net carbon sequestration is declining over time. The net carbon sequestration during 2015–2050 would increase by 30.2 to 218.3 million tonnes of CO2, when carbon price increases from 170SEK to 1428SEK per tonne of CO2. The associated cost, in terms of reduced total benefits of timber and other non-timber goods, ranges from 80SEK to 105.8SEK per tonne of CO2. The change in carbon sequestration (as compared with the baseline case) beyond 2050 is small when carbon price is 680SEK per tonne of CO2 or lower. With a carbon price of 1428SEK per tonne of CO2, carbon sequestration will increase by 70 million tonnes of CO2 from the baseline level during 2050-2070, and by 64 million tonnes during 2070–2170.