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International shipping currently accounts for about 3% of total global greenhouse gas (GHG) emissions, but would continue to rise as transport capacity expands. If the shipping industry aims at delivering its proportionate contribution to curbing global warming under the Paris agreement, the sector has to, inevitably, promote energy conservation and emission reduction. A rapidly growing oceangoing fleet size and correspondingly rising GHG emissions on a global scale raise an interesting research question: could a certain relationship between the two be characterized as a function so that further emissions can be forecast based on the model? The paper adopts an allometric approach based on biological scaling laws to explore the potential relationship between the fleet size and corresponding GHG emissions from shipping. The results show that both the slowdown of the navigation speed and the current implementation of the Energy Efficiency Design Index (EEDI) and Energy Efficiency Operation Index (EEOI) are effective on the whole. By employing the model, the development trends of GHG emissions from shipping in the future can be better understood. Through model applications and result analysis, numerical results validate the effectiveness of this method. The paper not only studies the development of GHG emissions from shipping in the past, but aslo evaluates its specific emission quantities in the future which is in line with the GHG emission reduction targets proposed by IMO on the 72nd IMO meeting, which will be helpful for policy decisions on the quota of GHG emissions to the International Maritime Organization (IMO) and port administrators.