The numerical sign problem has been a major obstacle to first-principles calculations of many important systems, including QCD at finite density. The worldvolume tempered Lefschetz thimble method is a HMC algorithm which solves both the sign problem and the ergodicity problems simultaneously. In this algorithm, configurations explore the extended configuration space (worldvolume) that includes a region where the sign problem disappears and also a region where the ergodicity problem is mild. The computational cost of the algorithm is expected to be much lower than other related algorithms based on Lefschetz thimbles, because one no longer needs to calculate the Jacobian of the gradient flow of Picard and Lefschetz when generating configurations. In this talk, after reviewing the basics of the method, we apply the method to various lattice field theories suffering from the sign problem, and report on the numerical results together with the computational cost scaling with the lattice volume.