Plasmons in two-dimensional (2D) materials beyond graphene have recently gained much attention. However, the experimental investigation is limited due to the lack of suitable materials. Here, we experimentally demonstrate localized plasmons in a correlated 2D charge-density-wave (CDW) material: 2H-TaSe2. The plasmon resonance can cover a broad spectral range from the terahertz (40 {mu}m) to the telecom (1.55 {mu}m) region, which is further tunable by changing thickness and dielectric environments. The plasmon dispersion flattens at large wave vectors, resulted from the universal screening effect of interband transitions. More interestingly, anomalous temperature dependence of plasmon resonances associated with CDW excitations is observed. In the CDW phase, the plasmon peak close to the CDW excitation frequency becomes wider and asymmetric, mimicking two coupled oscillators. Our study not only reveals the universal role of the intrinsic screening on 2D plasmons, but also opens an avenue for tunable plasmons in 2D correlated materials.