We study entanglement for a coupled harmonic oscillator system both discrete-time level and continuous-time level through the linear entropy (LE). We find that the nature of entanglement is drastically different between these two levels of the time structure. In the continuous-time case, we find that LE increases with the increasing of coupling constant and the system slowly gets into a maximally entangled state at extremely large value of coupling constant. In contrast, in the discrete-time case, we find that LE decreases with the increasing of a coupling constant and is zero at a critical value of the coupling constant. After that LE will increase again with the increasing of the coupling constant and the system suddenly gets into a maximally entangled state at a particular value of the coupling constant called a cut-off value. We also find that the nature of entanglement at discrete-time level and continuous-time level eventually becomes identical under the continuum time limit. This result of study shows that the system at discrete-time level exhibits much more intriguing phenomena than the one at continuous-time level.