To obtain the superiority property of solving time-varying linear matrix inequalities (LMIs), three novel finite-time convergence zeroing neural network (FTCZNN) models are designed and analyzed in this paper. First, to make the Matlab toolbox calculation processing more conveniently, the matrix vectorization technique is used to transform matrix-valued FTCZNN models into vector-valued FTCZNN models. Then, considering the importance of nonlinear activation functions on the conventional zeroing neural network (ZNN), the sign-bi-power activation function (AF), the improved sign-bi-power AF and the tunable sign-bi-power AF are explored to establish the FTCZNN models. Theoretical analysis shows that the FTCZNN models not only can accelerate the convergence speed, but also can achieve finite-time convergence. Computer numerical results ulteriorly confirm the effectiveness and advantages of the FTCZNN models for finding the solution set of time-varying LMIs.