The photon-added nonlinear coherent states, defined as a†m|α, f〉 up to a normalization constant, are still nonlinear coherent states with the nonlinear function f(N−m)[1−m/(N +1)]. Here |α, f〉 is the nonlinear coherent state with the nonlinear function f(N), N is the number operator, a is the boson creation operator and m is a non-negative integer. We introduce a new type of nonlinear coherent ...