In this work, we investigate the existence of one zero texture and one vanishing subtrace in the Majorana neutrino mass matrix. There are a total of thirty-six possible textures of neutrino mass matrix with the constrained conditions of one zero texture and one vanishing subtrace. Here we explore the phenomenological implications of only two classes of textures, i.e., Class A and Class B. We analyze the viability of all the textures using the ratio of the solar and atmospheric mass-squared differences ( \(R_{\nu }\) ). Out of 12 textures of both the classes, only one texture ( \(A_1\) ) from class A and three textures ( \(B_1\) , \(B_4\) and \(B_5\) ) from class B are found to be viable under the current neutrino oscillation data at \(3\sigma \) confidence level. Finally, we study the ranges of the Majorana Phases ( \(\alpha \) and \(\beta \) ) for the allowed range of the Dirac CP phase, \(\delta \) for all the viable textures.