We investigated noise spectra in the GHz range of tunneling magnetoresistive (TMR) read heads with resistance area product (RA) values of 4.0 and 1.7 Ω·μm² in order to understand the influence of spin torque on the noise in these TMR heads. Strong noise spectral peaks were observed at 4.2 and 6.5 GHz in TMR heads with respective RA values of 4.0 and 1.7 Ω·μm². Each peak intensity was enhanced with increasing external magnetic field depending on its polarity when bias current flowed from a free layer to reference one. These results mean that the spin torque influences the thermally excited magnetization fluctuation noise (thermal mag-noise) from the free layers. The peak became sharper and its intensity was enhanced with increasing current density up to 2.7 × 10¹¹ A/m² depending on its direction when the magnetization of free and reference layers were nearly anti-parallel to each other. These results demonstrate that the influence of spin torque on the thermal mag-noise becomes stronger as the current density increases.