With the increase of big data, solving Lasso problem becomes top research field. Past methods could not satisfy the time and efficient problem under big data situation. In order to deal with difficulty of computation and storage bringing from huge-scale and high-dimension data, this paper analyze the recent Lasso algorithm from three aspects: one-order method, random, and parallel and distributed computation, which play an important roles in dealing with huge-scale data problem. Based on those three aspects, this paper introduces and analyzes the novel algorithms: gradient descent method, Alternating Direction method of multipliers (ADMM), and coordinate descent method. Gradient descent method combine one order method and Nesterov's accelerate and smoothing method；ADMM put the random algorithm into the recent research; Coordinate descent make use of the character of coordinate system incorporation one-order method, random, and parallel and distributed computation. Moreover, this paper makes a deep analysis and research from primal and dual objective function.