In the field of engineering and economics, many data sequences have strong oscillation. These oscillating sequences, represented by interval numbers, will contain more information. The ternary interval number not only contains the upper and lower bounds of the system characteristics, but also contains a preference value. It has a good application value to study the prediction of the sequence of ternary interval numbers. In order to make the multivariable grey model GM(0, N) be able to directly model the ternary interval number sequence, the parameter setting of the GM(0, N) model equation is improved. The global contribution coefficient and lag coefficient are taken as the exact number. The linear correction term coefficient and compensation coefficient are set as the ternary interval numbers to compensate the different boundary points of the ternary interval number. Furthermore, to improve the prediction accuracy of the oscillatory sequence, the prediction sequence of the model is modified with the Markov prediction and sequence transformation method. By forecasting China's electricity consumption and total retail sales of consumer goods, the comparison results show that the ternary interval number multivariate grey model presented in the paper is better than the single variable grey model and the method of forecasting after converting interval number series into exact number series.