The individual modes and asymptotic parameters are important characteristics of stellar oscillation. Using TESS 2 minute cadence data from Sectors 1 to 75, we perform asteroseismic analysis of 687 red giants, and provide their oscillation mode parameters. The mode parameters, including frequencies {nu}n,l, amplitudes A_n,l_, and line widths {Gamma}n,l, are obtained through Markov Chain Monte Carlo fitting. The median uncertainty for frequency is 0.047{mu}Hz. Using the radial mode frequencies, we calculate the values of {Delta}{nu}, and derive asymptotic parameters ({epsilon}p, {epsilon}c, {delta}{nu}0l, q, and {Delta}{Pi}1) based on l=0,1,2 modes. For red giants with {Delta}{nu}>15.6{mu}Hz, there is a weaker correlation between {delta}{nu}02 and {Delta}{nu}, and a stronger mass dependence, compared to stars with lower {Delta}{nu}. Additionally, the ratio {delta}{nu}02/{Delta}{nu} presents a pronounced increase with {Delta}{nu} decrease, as these stars undergo rapid core contraction and their convective envelopes extend deep into the interior. At this stage, the ratio {delta}{nu}02/{Delta}{nu} may serve as a robust indicator for diagnosing the location of the convective boundary. Furthermore, the {epsilon}c values can be a potential index to distinguish red clump (RC) and secondary RC stars from red giant branch stars in the TESS field.

Cone search capability for table J/ApJS/279/37/table2 (Stellar oscillation parameters)