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A new concept of near semicompactness is introduced in L-fuzzy topological spaces, where L is a fuzzy lattice. It is weaker than semicompactness and is stronger than S*-closedness. It is described with collection of semiclosed L-fuzzy subsets and finite p-level semiregular-semiopen cover. It is a good L-extension; it is hereditary for semiregular-semiclosed L-fuzzy subsets and semiclopen L-fuzzy subsets; it is finitely additive and invariant under almost irresolute and almost irresolute-open mappings.