For low-carbon multimodal transportation planning problem with fuzzy demand (LCMTPP-FD) under the low-carbon background, the work aims to construct a mathematical model to minimize the cost, and transform the LCMTPP-FD by combining existing policies, such as mandatory carbon emission, carbon tax, carbon trading and carbon offset, so as to study the impact of different low-carbon policies on logistics costs and carbon emissions. According to the characteristics of the model, a sparrow search algorithm with t distribution was designed to solve the model under different low-carbon policies, and the number of iterations was taken as the degree of freedom of t distribution to improve the performance of the sparrow algorithm. The improved algorithm and several models were applied to a real transportation case. The improved sparrow algorithm could obtain the optimal solution in a short time, and the minimum carbon emission under the mandatory carbon emission was 9 522.28. The costs under the carbon trading and carbon offset policies were reduced by 11.41% and 17.24%, respectively. The experimental results show that the improved sparrow search algorithm has high convergence and search ability. Moreover, mandatory carbon emission can effectively reduce carbon emissions. Carbon trading and carbon offset can reduce the total costs, which are suitable for the promotion phase of low-carbon transportation.