On the basis of cone jet-algorithm, a Monte Carlo study of the properties of (mini) jets in high energy hadron-hadron cousions is carried out. Using the jetty frame, in which the momentum of jet is chosen as Z axis, the distributions of physical quantities inside jets-multiplicity, pseudorapidity, azimuthal angle and transverse momentum are obtained. The pseudorapidity distribution is asymetric, concentrating in the forward direction, which means that all the particles in the jet are moving forward in the direction of the total momentum of jet. This is further proved by a particle-momenta plot in the axial coordinate which shows that the jets look like sharp arrows with small forward-pointing feathers at the ends. The transverse momentum distribution for the event sample with respect to the direction of incident hadrons diviates from an exponential distribution considerably, in consistent with the productuon of (mini-)jets, while that inside jets with respect to the jet axis is basically an exponential. This means that the production of (mini-) jets is hard process, while the developement of jets is basically soft. These results show that cone algorithm is an effective method for the study of hard and semi-hard processes in high energy hadron-hadron and relativistic heavy ion collisions. It is found through the comparison of the distributions in jetty events and no-jet events that Et = 2GeV is a more reasonable cut for the cone algorithm in finding jets.