The invention discloses a filter-pressing type grouting device for a soft formation and a grouting method. The device comprises a thin grout inlet pipe, a perforated pipe, a variable-diameter contraction pipe, a casing pipe and a thick grout pipe; multiple pipe body holes are formed in the pipe wall of the perforated pipe, the perforated pipe is provided with a filter layer covering all the pipe body holes, the thin grout inlet pipe is connected with the upper end of the perforated pipe, the large-diameter end of the variable-diameter contraction pipe is connected with the lower end of the perforated pipe, the small-diameter end of the variable-diameter contraction pipe is connected with the thick grout pipe, the casing pipe is arranged outside the perforated pipe in a sleeving mode, and the lower end of the casing pipe is connected with the variable-diameter contraction pipe in a sealing mode. The method comprises the steps that 1, a grouting material is prepared; 2, the thick grout pipe is put into a grouting hole, and the lower end of the thick grout pipe is connected with a grouting pipe to reach the hole bottom; 3, cement grout with the pressure value of 0.5-0.8 MPa is delivered to the perforated pipe through the thin grout inlet pipe, the pressure rises as a congestion effect is formed in the variable-diameter contraction pipe, water is filtered out through the filter layer, thin grout is converted into thick grout in the device, and the water which is filtered out is drained through draining pipes; 4, the thin grout is converted into the thick grout in the device, the pressure is increased to 1-2 MPa, and then the thick grout is pressed into the formation.