The Hubbard model is a fundamental model to understand the superconductivity in cuprates. The ground state of the Hubbard model for the moderate interaction and weak doping has been shown a striped state. We study the superconductivity (SC) in the Hubbard and the t'-Hubbard model by using density matrix renormalization group (DMRG) and auxiliary field quantum Monte Carlo (AFQMC). I will first show that the ground state in Hubbard model, although presents d_{x^2+y^2} pairing, does not have long-range superconductivity. I will then discuss the pairing in the t'-Hubbard model, especially related to the recent discovery of quasi-long-range SC in the t'- Hubbard model on the 4-leg cylinders.