Summary: In this study, the bound state energy eigenvalues and the corresponding wave functions of the deformed Pöschl-Teller and hyperbolic Kratzer-like potentials have been obtained by the Nikiforov-Uvarov method using the deformed hyperbolic functions \((\text{sinhq} (x)=1/2(ex-qe-x), \text{coshq} (x)= 1/2(ex+qe-x), \text{sechq} (x)=1/\text{coshq} (x)\) and \(\text{tanhq} (x)=\text{sinhq} (x)/\text{coshq} (x))\) that were introduced for the first time by \textit{A. Arai} [J. Math. Anal. Appl. 158, No. 1, 63--79 (1991; Zbl 0731.47055)]. It is also observed that, the energy eigenvalues of these ``new'' type deformed hyperbolic potentials bring up the criteria for the shape invariance of the potentials according to the deformation parameter \(q\).