Hydrogen‐rich materials synthesized at megabar pressures have revolutionized the field of high‐temperature superconductivity. Among hydrogen‐rich materials, clathrate hydrides which show near‐room‐temperature superconductivity have been discovered in recent years. Herein, clathrate actinide hydrides are constructed, and their electronic properties and electron–phonon interaction as well as superconductivity under high pressures are theoretically investigated with density functional theory tools. The calculations adopt projected‐augmented‐wave (PAW) approach. The Perdew–Burke–Ernzerhof (PBE)‐type generalized gradient approximation (GGA) is used for the exchange–correlation potentials. Specifically, Th–H and Pu–H compounds are presented, of which the stability is demonstrated via calculated phonon dispersions, and the superconducting transition temperatures Tc under 100, 200, and 400 GPa are estimated. ThH10 among Th–H compounds has the highest transition temperature of superconductivity, and Tc of ThH10 can reach 151.8 K under 200 GPa. PuH10 is also better than other investigated Pu–H compounds in superconductivity, but the highest Tc of PuH10 is only 31.4 K under 400 GPa, much lower than that of ThH10.