Context : We introduce the Dwarf Galaxy Survey with Amateur Telescopes ( DGSAT ) project and report the discovery of eleven low surface brightness ( LSB ) galaxies in the fields of the nearby galaxies NGC 2683 , NGC 3628 , NGC 4594 ( M104 ) , NGC 4631 , NGC 5457 ( M101 ) , and NGC 7814 . Aims : The DGSAT project aims to use the potential of small-sized telescopes to probe LSB features around large galaxies and to increase the sample size of the dwarf satellite galaxies in the Local Volume . Methods : Using long exposure images , fields of the target spiral galaxies are explored for extended low surface brightness objects . After identifying dwarf galaxy candidates , their observed properties are extracted by fitting models to their light profiles . Results : We find three , one , three , one , one , and two new LSB galaxies in the fields of NGC 2683 , 3628 , 4594 , 4631 , 5457 , and 7814 , respectively . In addition to the newly found galaxies , we analyse the structural properties of nine already known galaxies . All of these 20 dwarf galaxy candidates have effective surface brightnesses in the range 25.3 \lesssim \mu _ { e } \lesssim 28.8 mag.arcsec ^ { -2 } and are fit with Sersic profiles with indices n \lesssim 1 . Assuming that they are in the vicinity of the above mentioned massive galaxies , their r -band absolute magnitudes , their effective radii , and their luminosities are in the ranges -15.6 \lesssim M _ { r } \lesssim - 7.8 , 160 pc \lesssim R _ { e } \lesssim 4.1 kpc , and 0.1 \times 10 ^ { 6 } \lesssim \left ( \frac { L } { L _ { \odot } } \right ) _ { r } \lesssim 127 \times 1 % 0 ^ { 6 } , respectively . To determine whether these LSB galaxies are indeed satellites of the above mentioned massive galaxies , their distances need to be determined via further observations . Conclusions : Using small telescopes , we are readily able to detect LSB galaxies with similar properties to the known dwarf galaxies of the Local Group .