The invention discloses a weft yarn curve tatting fabric weaving method and a dedicated elastic free reed. A weft yarn of a woven fabric is in a curve shape; the weaving method comprises the following steps: pacing of warp, opening, weft insertion, battening and reeling, and is characterized in that the elastic free reed, of which the reed teeth are bent according to a battening force, is adopted in battening; by utilizing change of a fabric texture or change of thickness of the weft yarn, full ratios on the same line in a weft direction of the woven fabric on a weaving machine differ, and the condition that battening forces differ is caused; when the elastic free reed is subjected to battening, the reed teeth are bent according to the magnitude of the battening force; if the full ratio is large, the reed teeth bending degree is large; and if the full ratio is small, the reed teeth bending degree is small, so that a weft yarn curve is realized. With the adoption of the weft yarn curve tatting fabric weaving method and the dedicated elastic free reed, the traditional, transverse, horizontal and vertical weaving manner is changed, the woven fabric weft yarn is in a curve shape; if colored lines are used, a beautiful curve pattern is generated, so that the grade of tatting fabric varieties can be improved.