Phosphate (P i) and temperature are two important environmental factors affecting algal growth and the occurrence of red tide. In this paper, we conduct experiments on Karenia mikimotoi under different P i concentrations and temperatures and propose a novel P i uptake model by incorporating Arrhenius function and P i -stress function into the two-stage model presented in one of our recent paper (Jiang et al. (2019)). In both P i -replete and P i -deplete, the model parameters are obtained by fitting the experimental data at 24 °C and validated by the experimental data at 20 °C, respectively. K. mikimotoi under low P i condition entered into the exponential growth phase earlier compared with P i -replete groups. Under the P i -replete condition, K. mikimotoi continually increased, while the P i -deplete condition showed a wave trend. The experimental results and the fitting of experimental data both show that K. mikimotoi has an obvious response to temperature. In both P i -replete and P i -deplete, the peak values of the cell quota of intracellular P i and surface-adsorbed P i at 24 °C were higher than those at 20 °C. Using the luxury coefficient and growth potential, interspecific competition between K. mikimotoi and Prorocentrum donghaiense is also discussed. These results and conclusions are helpful to understand the P i uptake characteristics of algae at different P i concentrations and temperatures, and could effectively explain mechanisms of interspecific competition and succession between different algae species during red tide. • A novel two-stage model for uptake kinetics of phosphate by algae is proposed. • Karenia mikimotoi has an obvious response to P i concentration and temperature. • The interspecific competition between two different algae species is discussed. • The results are helpful to understanding the P i uptake characteristics of algae. [ABSTRACT FROM AUTHOR]