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In this paper, we introduce a distributed algorithm that is specifically designed to tackle the least-squares problem within a network system of linear algebraic equations. Our focus is on static directed multi-agent networks, where each agent possesses knowledge of a distinct subset of the linear equations. Furthermore, we examine a scenario where agents lack information about their "out-degrees" at any given time. By imposing the strong connectivity condition on the communication network, we establish that the local estimated solution of each agent exhibits exponential convergence towards the least-squares solution of the corresponding network system of linear algebraic equations. • A consensus based distributed algorithm is devised to solve the least-squares problem. • The technique solves LS estimation over directed networks where agents lack out-degree info. • Achieves rapid exponential convergence to the least-squares solution. • Simulation confirms algorithm's theory, shows improvements over existing methods. [ABSTRACT FROM AUTHOR]