Modern pulse compression radar involves digital signal processing of high bandwidth pulses modulated with different coding schemes. One of the limiting factors in the radar’s design to achieve desired target range and resolution is the need of high rate analog-to-digital (A/D) conversion fulfilling the Nyquist sampling criteria. The high sampling rates necessitate huge storage capacity, more power consumption, and extra processing requirement. We introduce a new approach to sample wideband radar waveform modulated with Costas sequence at a sub-Nyquist rate based upon the concept of compressive sensing (CS). Sub-Nyquist measurements of Costas sequence waveform are performed in an analog-to-information (A/I) converter based upon random demodulation replacing traditional A/D converter. The novel work presents an 8-order Costas coded waveform with sub-Nyquist sampling and its reconstruction. The reconstructed waveform is compared with the conventionally sampled signal and depicts high-quality signal recovery from sub-Nyquist sampled signal. Furthermore, performance of CS-based detections after reconstruction are evaluated in terms of receiver operating characteristic (ROC) curves and compared with conventional Nyquist-rate matched filtering scheme.