This paper considers the problem of frequency estimation for a multi-sinusoidal signal consisting of n sinuses in finite-time. The parameterization approach based on applying delay operators to a measurable signal is used. The result is the nth order linear regression model with n parameters, which depends on the signals frequencies. We propose to use Dynamic Regressor Extension and Mixing method to replace nth order regression model with n first-order regression models. Then the standard gradient descent method is used to estimate separately for each the regression model parameter. On the next step using algebraic equations finite-time frequency estimate is found. The described method does not require measuring or calculating derivatives of the input signal, and uses only the signal measurement. The efficiency of the proposed approach is demonstrated through the set of numerical simulations.