This　paper　presents　a　new　robust　sliding　mode　control　(SMC)　method　with　well-developed　theoretical　proof　for　general　uncertain　time-varying　delay　stochastic　systems　with　structural　uncertainties　and　the　Brownian　noise　(Wiener　process).　The　key　features　of　the　proposed　method　are　to　apply　singular　value　decomposition　(SVD)　to　all　structural　uncertainties　and　to　introduce　adjustable　parameters　for　control　design　along　with　the　SMC　method.　It　leads　to　a　less-conservative　condition　for　robust　stability　and　a　new　robust　controller　for　the　general　uncertain　stochastic　systems　via　linear　matrix　inequality　(LMI)　forms.　The　system　states　are　able　to　reach　the　SMC　switching　surface　as　guaranteed　in　probability　1.　Furthermore,　it　is　theoretically　proved　that　the　proposed　method　with　the　SVD　and　adjustable　parameters　is　less　conservatism　than　the　method　without　the　SVD.　The　paper　is　mainly　to　provide　all　strict　theoretical　proofs　for　the　method　and　results.　©　2014,　South　China　University　of　Technology,　Academy　of　Mathematics　and　Systems　Science,　Chinese　Academy　of　Sciences　and　Springer-Verlag　Berlin　Heidelberg.