This paper introduces a method for automatic composition of semantic web services using linear logic theorem proving. The method uses semantic web service language (DAML-S) for external presentation of web services, and, internally, the services are presented by extralogical axioms and proofs in linear logic. Linear logic(LL)[2], as a resource conscious logic, enables us to define the attributes of web services formally (in particular, qualitative and quantitative value of non-functional attributes). The subtyping rules that are used for semantic reasoning are presented as linear logic implication. We propose a system architecture where the DAML-S parser, linear logic theorem prover and semantic reasoner can work together. This architecture has been implemented in Java programming language.