Long spreading code and BOC (Binary Offset Carrier) modulation technique are used in the next generation GNSS (Global Navigation Satellite System) to improve positioning performance and to reduce inter-GNSS interference, however, the signal acquisition process of a GNSS receiver can take longer time and require additional hardware resources than legacy GPS receivers. This paper presents BOC-TDCC (Two-Dimensional Compressed Correlator) technique for the fast acquisition of the next generation GNSS signals. In the proposed BOC-TDCC, signal power in neighboring code phase hypotheses and Doppler frequency hypotheses can be coherently combined and tested by a single compressed correlator in the 1st stage, and conventional correlator based serial search technique is employed in the 2nd stage to test each hypothesis combined in the 1st stage. The performance of the BOC-TDCC is demonstrated with numerous Monte Carlo simulations and tested with real data. The BOCTDCC has much lower mean acquisition time (MAT) than other conventional search schemes, which demonstrates that the BOCTDCC is an effective search scheme for the next generation GNSS signals