In order to reduce the compression power and to use the overall energy contained in LNG effectively, a combined cycle is devised and simulated. The combined cycle is composed of two cycles; one is an open cycle of liquid/solid carbon dioxide production cycle utilizing LNG cold energy in $CO_2$ condenser and the other is a closed cycle gas turbine which supplies power to the $CO_2$ cycle, utilizes LNG cold energy for lowering the compressor inlet temperature, and uses the heating value of LNG at the burner. The power consumed for the $CO_2$ cycle is investigated in terms of a production ratio of solid $CO_2$. The present study shows that much reduction in both $CO_2$ compression power (only $35\%$ of power used in conventional dry ice production cycle) and $CO_2$ condenser pressure could be achieved by utilizing LNG cold energy and that high cycle efficiency ($55.3\%$ at maximum power condition) in the gas turbine could be accomplished with the adoption of compressor inlet cooling and regenerator. Exergy analysis shows that irreversibility in the combined cycle increases linearly as a production ratio of solid $CO_2$ increases and most of the irreversibility occurs in the condenser and the heat exchanger for compressor inlet cooling. Hence, incoming LNG cold energy to the above components should be used more effectively.