Chemotaxis is an important biological mechanism in the nature. We prove the existence of spiky steady states of the one-dimensional continuous chemotaxis model with logarithm sensitivity in a more general case by using global bifurcation theory with chemotactic coefficient being the bifurcating parameter and by studying the asymptotic behavior of the steady states as the chemotactic coefficient goes to infinity. One can use spiky steady states to model the cell aggregation, which is one of the most important phenomenon in chemotaxis.