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For an implicit scheme I want to solve system $Ax=B$, where $A$ is a non-symmetric square matrix. I want source codes of large sparse matrix solvers (e.g. LU-SGS) to use in my code which is in C language. I have tried preconditioned GMRES code from this site but its getting slow and takes huge amount of memory(sometimes program is getting "killed" automatically).

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I would look at PETSc and Trilinos. They have tons of different sparse solvers available.

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You didn't say how big your system of equations is. But if you are interested in trying direct sparse solvers, here are links to two for non-symmetric systems that are known to be of high quality and are written in C.

SuiteSparse SuperLU

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  • $\begingroup$ This link is very useful. Thank you very much. $\endgroup$
    – Shainath
    Jun 11, 2013 at 13:00
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I highly recommend on Eigen. You can also look at taucs.

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