This is a very difficult question to answer as there is no completely fool-proof way in which to define what is and is not a country. Palestine is seen by many as a country, but it lacks some of the most important attributes of a country.
On the one hand, most of the countries of the world recognize Palestine as a country. More than two-thirds of the countries that are members of the United Nations have recognized Palestine as a country. There was a vote held recently in the UN in which Palestine was given status as a non-member observer state. There are, then, many countries and organizations that see Palestine as a country. The United States, Canada, and the countries of the European Union, however, are among those that do not recognize Palestine.
On the other hand, Palestine lacks some very important aspects of a true country. The most important of these is the fact that it does not have any ability to keep another country, Israel, from occupying its territory or from controlling access to that territory. Israel occupied the Gaza Strip for years. It continues to refuse to allow many kinds of goods to enter Gaza. It blockades Gaza from the sea. It continues to build settlements on Palestinian land in the West Bank.
So, Palestine is recognized as a country by many other countries, but it is not able to truly act as a sovereign state.