This paper presents convergence analysis of Jacobi iterative method using logarithmic number system (LNS) for solving linear systems, where multiplications and divisions are replaced with additions and subtractions, respectively. Two major factors are identified and considered in our convergence analysis. First, in any hardware architecture for Jacobi iterative method, only a set of unknowns can be processed in parallel due to the constraint of hardware resources. Secondly, the conversions of ogarithm-to-floating point and floating-to-logarithm introduce additional error. The convergence analysis demonstrates to what extent the hardware resource constraints and additional conversion error affect the convergence of Jacobi iterative method.