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High order harmonic generation towards attosecond XUV pulse emission in a precisely shaped laser field,either with two color or single color double driving laser pulses was intensively investigated,both theoretically and experimentally.We demonstrated a novel scheme of chirp control by exploiting the dispersion characteristic controlled by the laser field,which is referred as the dynamic compensation of chirp here in this work,different from previous approaches based on the static dispersion of the materials.To control the material dispersion dynamically,we add a weak second harmonic laser pulse to the fundamental driving laser pulse for HHG.The demonstrated method,as opposed to other demonstrated methods,can provide positive chirp.Using this technique,we have compensated the negative chirp for the first time.Additionally it has the advantage that the chirp of the attosecond pulses can be varied easily and continuously by simply changing the time delay between the two color pulses,which could open new opportunities for attosecond coherent control.