We consider the following triple power nonlinear Schrödinger equation: iut + ∆u + a 1 |u|u + a 2 |u| 2 u + a 3 |u| 3 u = 0. We are interested in algebraic standing waves i.e standing waves with algebraic decay above equation in dimensions n (n = 1, 2, 3). We prove the instability of these solutions in the cases DDF (we use abbreviation D: defocusing (a i < 0), F: focusing (a i > 0)) and DFF when n = 2, 3 and in the case DFF with a 2 < 32 15 √ 6 when n = 1. In the case DFD, we only obtain an existence result of algebraic solution in dimension one.