A nickel-cobalt (NiCo) layered double hydroxide (LDH) saturable absorber (SA) was successfully fabricated and utilized as a passively mode-locked (PML) laser modulator for the first time. We successfully investigated a 1.34 µm passively Q-switched (PQS) and Q-switched mode-locked (QML) laser operation of Nd:Lu0.15Y0.85VO4 mixed crystal with NiCo-LDH SA, respectively. A stable pulse sequence with a narrowest pulse width of 52 ns and a repetition frequency of 1.18 MHz was obtained, leading to a single pulse energy of 0.72 µJ. Furthermore, for the QML laser operation, an average power of 1.10 W and a calculated pulse width of 25 ps were gained with a repetition frequency of 134 MHz. The results indicate the NiCo-LDH SA has remarkable nonlinear optical properties and promising application prospects in the field of laser modulators at 1.3 µm.