This paper develops a new algorithm for learning densely connected sub-Gaussian linear structural equation models (SEMs) in high-dimensional settings, where the number of nodes increases with increasing number of samples. The proposed algorithm consists of two main steps: (i) the component-wise ordering estimation using ℓ2-regularized regression and (ii) the presence of edge estimation using ℓ1-regularized regression. Hence, the proposed algorithm can recover a large degree graph with a small indegree constraint. Also proven is that the sample size n=Ω(p) is sufficient for the proposed algorithm to recover a sub-Gaussian linear SEM provided that d=O(plogp), where p is the number of nodes and d is the maximum indegree. In addition, the computational complexity is polynomial, O(np2max(n,p)). Therefore, the proposed algorithm is statistically consistent and computationally feasible for learning a densely connected sub-Gaussian linear SEM with large maximum degree. Numerical experiments verified that the proposed algorithm is consistent, and performs better than the state-of-the-art high-dimensional linear SEM learning HGSM, LISTEN, and TD algorithms in both sparse and dense graph settings. Also demonstrated through real data is that the proposed algorithm is well-suited to estimating the Seoul public bike usage patterns in 2019.