Let S0 be a bordered Riemann surface of finite type, and let T(S0) (resp. T R (S0)) be the Teichmuller space (resp. reduced Teichmuller space) of S0. The length spectrum function defines a metric on T R (S0) but not on T(S0). In this paper, we introduce a modified length spectrum function that does define a metric on T(S0). Then we show that if two points of T(S0) are close in the Teichmuller metric then they are close in the modified length spectrum metric, but the converse is not true. We also prove that T(S0) is not complete under this modified length spectrum metric.