A mode-hop-free tunable external-cavity Littrow diode laser with intracavity acousto-optic modulators (AOMs) has been built. The modes of the red laser diode without a special antireflection coating are shifted by varying the injection current. The external resonator modes and the grating selectivity are independently electrically alterable by two AOMs. Thus, a tuning of the external resonator over up to $1900\mathrm{GHz}$ is possible. A precise computer control of laser diode and AOMs allowed a single-mode tuning of the whole laser with a tuning range of $225\mathrm{GHz}$ in $250\mathrm{s}$ . Additionally, we demonstrated fast tuning over $90\mathrm{GHz}$ in $190\mathrm{\mu }\mathrm{s}$ and a repetition rate of $2.5\mathrm{kHz}$ .