This paper describes an efficient implementation of a form of linear semi-infinite programming (LSIP). We look at maximizing (minimizing) a linear function over a set of constraints formed by positive trigonometric polynomials. Previous studies about LSIP are formulated using semi-definite programming (SDP), this is typically done by using the Kalman Yakubovich Popov (KYP) lemma or using a trace operation involving a Grammian matrix, which can be computationally expensive. The proposed algorithm is based on simplex method that directly solves the LSIP without any parameterization. Numerical results show that the proposed LISP algorithm is significantly more efficient than existing SDP solvers using KYP lemma and Grammian matrix, in both execution time and memory.