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In this paper, we consider a kind of delayed Schoener's competition model with harvesting terms and impulsive effects. By means of Mawhin's continuation theorem of coincidence degree theory, some sufficient conditions are obtained for the existence of at least four positive almost periodic solutions for the above model. Further, by using the comparison theorem and constructing a suitable Lyapunov functional, the global asymptotic stability of the model is also investigated. To the best of the author's knowledge, sofar, the results of this paper are completely new. An example and numerical simulations are employed to illustrate the main results in this paper. [ABSTRACT FROM AUTHOR]